Question 1

Subtract. Simplify, if possible.
- 221x−415x2\frac{2}{21 \mathrm{x}}-\frac{4}{15 \mathrm{x}^{2}}21x2​−15x24​

Accepted Answer

A)    −2315x2-\frac{2}{315 x^{2}}−315x22​ 
B)    −221x+15x2\frac{-2}{21 x+15 x^{2}}21x+15x2−2​ 
C)    8105x2\frac{8}{105 x^{2}}105x28​ 
D)    2(5x−14) 105x2\frac{2(5 x-14) }{105 x^{2}}105x22(5x−14) ​E) All of the above
F) A) and B)

Question 2

Add. Simplify, if possible.
- 2y2−3y+2+7y2−1\frac{2}{y^{2}-3 y+2}+\frac{7}{y^{2}-1}y2−3y+22​+y2−17​

Accepted Answer

A)    9y−12(y−1) (y−2) \frac{9 y-12}{(y-1) (y-2) }(y−1) (y−2) 9y−12​ 
B)    28y−12(y−1) (y+1) (y−2) \frac{28 \mathrm{y}-12}{(\mathrm{y}-1) (\mathrm{y}+1) (\mathrm{y}-2) }(y−1) (y+1) (y−2) 28y−12​ 
C)    12y−9(y−1) (y+1) (y−2) \frac{12 y-9}{(y-1) (y+1) (y-2) }(y−1) (y+1) (y−2) 12y−9​ 
D)    9y−12(y−1) (y+1) (y−2) \frac{9 y-12}{(y-1) (y+1) (y-2) }(y−1) (y+1) (y−2) 9y−12​E) A) and B)
F) B) and C)

Question 3

Multiply. Do not simplify.
- x−64−x⋅−1−1\frac{x-6}{4-x} \cdot \frac{-1}{-1}4−xx−6​⋅−1−1​

Accepted Answer

A)    (x−6) (−1) (4−x) (−1) \frac{(x-6) (-1) }{(4-x) (-1) }(4−x) (−1) (x−6) (−1) ​ 
B)    (x−6) (−1) 4−x\frac{(x-6) (-1) }{4-x}4−x(x−6) (−1) ​ 
C)    x−6(4−x) (−1) \frac{x-6}{(4-x) (-1) }(4−x) (−1) x−6​ 
D)    (4−x) (−1) (x−6) (−1) \frac{(4-x) (-1) }{(x-6) (-1) }(x−6) (−1) (4−x) (−1) ​E) B) and C)
F) A) and D)

Question 4

Multiply and, if possible, simplify.
- k2+14k+45k2+18k+81⋅k2+9kk2+11k+30\frac{\mathrm{k}^{2}+14 \mathrm{k}+45}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+11 \mathrm{k}+30}k2+18k+81k2+14k+45​⋅k2+11k+30k2+9k​

Accepted Answer

A)    kk+6\frac{\mathrm{k}}{\mathrm{k}+6}k+6k​ 
B)    k2+9kk+6\frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}+6}k+6k2+9k​ 
C)    1k+6\frac{1}{\mathrm{k}+6}k+61​ 
D)    kk2+18k+81\frac{\mathrm{k}}{\mathrm{k}^{2}+18 \mathrm{k}+81}k2+18k+81k​E) B) and C)
F) None of the above

Question 5

Find the LCM.
- 20,12,1520,12,1520,12,15

Accepted Answer

A)   30
B)   60
C)   12
D)   20 E) B) and D)
F) B) and C)

Question 6

Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Accepted Answer

Sure! So when we multiply rational expre...

Question 7

Find all numbers for which the rational expression is not defined.
- x2−16x2−7x+10\frac{x^{2}-16}{x^{2}-7 x+10}x2−7x+10x2−16​

Accepted Answer

A)    x=−5x=-5x=−5  and  x=−2x=-2x=−2 
B)    x=0x=0x=0 
C)    x=4x=4x=4  and  x=−4x=-4x=−4 
D)    x=5x=5x=5  and  x=2x=2x=2E) A) and C)
F) B) and C)

Question 8

Find all numbers for which the rational expression is not defined.
- 5y−4y2−49\frac{5 y-4}{y^{2}-49}y2−495y−4​

Accepted Answer

A)    y=7y=7y=7  and  y=−7y=-7y=−7 
B)    y=45y=\frac{4}{5}y=54​ 
C)    y=7y=7y=7 
D)    y=49y=49y=49E) A) and B)
F) All of the above

Question 9

Solve the equation.
- x−3x+6=47\frac{x-3}{x+6}=\frac{4}{7}x+6x−3​=74​

Accepted Answer

A)    4511\frac{45}{11}1145​ 
B)   1
C)   15
D)   3 E) B) and C)
F) A) and D)

Question 10

For $\mathrm{x} \neq 2$, the rational expression $\frac{6(\mathrm{x}-2)}{\mathrm{x}-2}$ is equal to 6 . Can the same be said for $\frac{6 x-2}{x-2}$ ? Explain why or why not.

Accepted Answer

No, the same cannot be said for the rati...

Question 11

Find the LCM.
- 6xy,15x26 x y, 15 x^{2}6xy,15x2

Accepted Answer

A)    30x3y30 x^{3} y30x3y 
B)    30xy330 x y^{3}30xy3 
C)    30x2y30 x^{2} y30x2y 
D)    30xy230 x y^{2}30xy2E) None of the above
F) A) and D)

Question 12

Find an equation of variation in which  yyy  varies inversely as  xxx  and the following is true.
- y=0.25y=0.25y=0.25 , when  x=32x=32x=32

Accepted Answer

A)    y=9xy=\frac{9}{x}y=x9​ 
B)    y=8xy=\frac{8}{x}y=x8​ 
C)    y=8xy=8 xy=8x 
D)    y=11xy=\frac{11}{x}y=x11​E) B) and D)
F) A) and D)

Question 13

Solve the problem.
-The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 42 minutes. If the two printers work together, how long would they take to print out the project?

Accepted Answer

A)    123512 \frac{3}{5}1253​  minutes
B)    563\frac{5}{63}635​  of a minute
C)   10 minutes
D)   126 minutes E) All of the above
F) A) and C)

Question 14

Simplify.
- 3m2+3m9m2+6m\frac{3 m^{2}+3 m}{9 m^{2}+6 m}9m2+6m3m2+3m​

Accepted Answer

A)    m+13m+2\frac{m+1}{3 m+2}3m+2m+1​ 
B)    m2+13m2+2\frac{m^{2}+1}{3 m^{2}+2}3m2+2m2+1​ 
C)    m+1m+2\frac{m+1}{m+2}m+2m+1​ 
D)    m+33m+2\frac{m+3}{3 m+2}3m+2m+3​E) C) and D)
F) B) and D)

Question 15

Find the LCM.
- x2−6x+5,4x−20x^{2}-6 x+5,4 x-20x2−6x+5,4x−20

Accepted Answer

A)    4(x+1) (x+5) 4(x+1) (x+5) 4(x+1) (x+5)  
B)    4(x−1) (x+5) 4(x-1) (x+5) 4(x−1) (x+5)  
C)    4(x+1) (x−5) 4(x+1) (x-5) 4(x+1) (x−5)  
D)    4(x−1) (x−5) 4(\mathrm{x}-1) (\mathrm{x}-5) 4(x−1) (x−5) E) C) and D)
F) All of the above

Question 16

Find the LCM.
- 7a+21,a2+3a7 a+21, a^{2}+3 a7a+21,a2+3a

Accepted Answer

A)    7a(a+3) 7 a(a+3) 7a(a+3)  
B)    7a2+37 \mathrm{a}^{2}+37a2+3 
C)    7a+37 a+37a+3 
D)    7a2+217 \mathrm{a}^{2}+217a2+21E) A) and D)
F) All of the above

Question 17

Solve the problem.
-The volume  VVV  of a gas varies inversely as the pressure  PPP  on it. The volume of a gas is  400 cm3400 \mathrm{~cm}^{3}400 cm3  under a pressure of  26 kg/cm226 \mathrm{~kg} / \mathrm{cm}^{2}26 kg/cm2 . Find an equation of variation.

Accepted Answer

A)    V=2P\mathrm{V}=\frac{2}{\mathrm{P}}V=P2​ 
B)    V=P10,400\mathrm{V}=\frac{\mathrm{P}}{10,400}V=10,400P​ 
C)    V=10,400P\mathrm{V}=\frac{10,400}{\mathrm{P}}V=P10,400​ 
D)    V=10,400P\mathrm{V}=10,400 \mathrm{P}V=10,400PE) B) and D)
F) B) and C)

Question 18

Simplify.
- 1a+11a−1\frac{\frac{1}{a}+1}{\frac{1}{a}-1}a1​−1a1​+1​

Accepted Answer

A)    1+a1−a\frac{1+a}{1-a}1−a1+a​ 
B)   1
C)    a1−a2\frac{\mathrm{a}}{1-\mathrm{a}^{2}}1−a2a​ 
D)    1−a21-\mathrm{a}^{2}1−a2E) A) and C)
F) A) and B)

Question 19

Find the LCM.
- 35x,5x2,7x335 x, 5 x^{2}, 7 x^{3}35x,5x2,7x3

Accepted Answer

A)    7x37 x^{3}7x3 
B)    35x335 x^{3}35x3 
C)    35x535 x^{5}35x5 
D)    35x235 x^{2}35x2E) A) and B)
F) B) and C)

Question 20

Add. Simplify, if possible.
- m2−8mm−2+12m−2\frac{m^{2}-8 m}{m-2}+\frac{12}{m-2}m−2m2−8m​+m−212​

Accepted Answer

A)    m+6m+6m+6 
B)    m\mathrm{m}m  - 2
C)    m2−8m+12m−2\frac{m^{2}-8 m+12}{m-2}m−2m2−8m+12​ 
D)    m−6m-6m−6E) A) and B)
F) None of the above

Exam 6: Rational Expressions and Equations

Solve the problem. -The volume VVV of a gas varies inversely as the pressure PPP on it. The volume of a gas is 400 cm3400 \mathrm{~cm}^{3}400 cm3 under a pressure of 26 kg/cm226 \mathrm{~kg} / \mathrm{cm}^{2}26 kg/cm2 . Find an equation of variation.

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Find an equation of variation in which yyy varies inversely as xxx and the following is true. - y=0.25y=0.25y=0.25 , when x=32x=32x=32

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Find the LCM. - 6xy,15x26 x y, 15 x^{2}6xy,15x2

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Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Correct AnswerAnswered by ExamLex AISure! So when we multiply rational expre...View AnswerShow Answer

Solve the problem. -The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 42 minutes. If the two printers work together, how long would they take to print out the project?

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Find all numbers for which the rational expression is not defined. - x2−16x2−7x+10\frac{x^{2}-16}{x^{2}-7 x+10}x2−7x+10x2−16​

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Find all numbers for which the rational expression is not defined. - 5y−4y2−49\frac{5 y-4}{y^{2}-49}y2−495y−4​

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Simplify. - 1a+11a−1\frac{\frac{1}{a}+1}{\frac{1}{a}-1}a1​−1a1​+1​

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Add. Simplify, if possible. - 2y2−3y+2+7y2−1\frac{2}{y^{2}-3 y+2}+\frac{7}{y^{2}-1}y2−3y+22​+y2−17​

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Subtract. Simplify, if possible. - 221x−415x2\frac{2}{21 \mathrm{x}}-\frac{4}{15 \mathrm{x}^{2}}21x2​−15x24​

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Find the LCM. - x2−6x+5,4x−20x^{2}-6 x+5,4 x-20x2−6x+5,4x−20

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Multiply. Do not simplify. - x−64−x⋅−1−1\frac{x-6}{4-x} \cdot \frac{-1}{-1}4−xx−6​⋅−1−1​

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Solve the equation. - x−3x+6=47\frac{x-3}{x+6}=\frac{4}{7}x+6x−3​=74​

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Add. Simplify, if possible. - m2−8mm−2+12m−2\frac{m^{2}-8 m}{m-2}+\frac{12}{m-2}m−2m2−8m​+m−212​

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Find the LCM. - 7a+21,a2+3a7 a+21, a^{2}+3 a7a+21,a2+3a

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Find the LCM. - 20,12,1520,12,1520,12,15

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Simplify. - 3m2+3m9m2+6m\frac{3 m^{2}+3 m}{9 m^{2}+6 m}9m2+6m3m2+3m​

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For x≠2\mathrm{x} \neq 2x=2 , the rational expression 6(x−2)x−2\frac{6(\mathrm{x}-2)}{\mathrm{x}-2}x−26(x−2)​ is equal to 6 . Can the same be said for 6x−2x−2\frac{6 x-2}{x-2}x−26x−2​ ? Explain why or why not.

Correct AnswerAnswered by ExamLex AINo, the same cannot be said for the rati...View AnswerShow Answer

Multiply and, if possible, simplify. - k2+14k+45k2+18k+81⋅k2+9kk2+11k+30\frac{\mathrm{k}^{2}+14 \mathrm{k}+45}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+11 \mathrm{k}+30}k2+18k+81k2+14k+45​⋅k2+11k+30k2+9k​

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Find the LCM. - 35x,5x2,7x335 x, 5 x^{2}, 7 x^{3}35x,5x2,7x3

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Solve the problem. -The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $400 \mathrm{~cm}^{3}$ under a pressure of $26 \mathrm{~kg} / \mathrm{cm}^{2}$ . Find an equation of variation.

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Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=0.25$ , when $x=32$

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Find the LCM. - $6 x y, 15 x^{2}$

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Find all numbers for which the rational expression is not defined. - $\frac{x^{2}-16}{x^{2}-7 x+10}$

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Find all numbers for which the rational expression is not defined. - $\frac{5 y-4}{y^{2}-49}$

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Simplify. - $\frac{\frac{1}{a}+1}{\frac{1}{a}-1}$

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Add. Simplify, if possible. - $\frac{2}{y^{2}-3 y+2}+\frac{7}{y^{2}-1}$

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Subtract. Simplify, if possible. - $\frac{2}{21 \mathrm{x}}-\frac{4}{15 \mathrm{x}^{2}}$

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Find the LCM. - $x^{2}-6 x+5,4 x-20$

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Multiply. Do not simplify. - $\frac{x-6}{4-x} \cdot \frac{-1}{-1}$

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Solve the equation. - $\frac{x-3}{x+6}=\frac{4}{7}$

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Add. Simplify, if possible. - $\frac{m^{2}-8 m}{m-2}+\frac{12}{m-2}$

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Find the LCM. - $7 a+21, a^{2}+3 a$

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Find the LCM. - $20,12,15$

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Simplify. - $\frac{3 m^{2}+3 m}{9 m^{2}+6 m}$

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For $\mathrm{x} \neq 2$ , the rational expression $\frac{6(\mathrm{x}-2)}{\mathrm{x}-2}$ is equal to 6 . Can the same be said for $\frac{6 x-2}{x-2}$ ? Explain why or why not.

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No, the same cannot be said for the rati...
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Multiply and, if possible, simplify. - $\frac{\mathrm{k}^{2}+14 \mathrm{k}+45}{\mathrm{k}^{2}+18 \mathrm{k}+81} \cdot \frac{\mathrm{k}^{2}+9 \mathrm{k}}{\mathrm{k}^{2}+11 \mathrm{k}+30}$

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Find the LCM. - $35 x, 5 x^{2}, 7 x^{3}$

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