Free Printable PCC Chapter 11 Review

1.

What is the least common multiple of $25x$ and $15x$ ?

a)

$5x$

b)

$5x^2$

c)

$75x$

d)

$375x^2$

2.

What is the least common multiple of $16x^{2\ }$ and $24x$ ?

a)

$384x^{3\ }$

b)

$48x^{2\ }$

c)

$48x$

d)

$8x$

3.

What is the least common multiple of $6x$ and $2\left(x-1\right)$ ?

a)

$12x\left(x-1\right)$

b)

$6\left(x-1\right)$

c)

$6x\left(x-1\right)$

d)

$2\left(x-1\right)$

4.

What is the least common multiple of $9x\left(x-1\right)$ and $12x$ ?

a)

$3x$

b)

$36x^2\left(x-1\right)$

c)

$108x\left(x-1\right)$

d)

$36x\left(x-1\right)$

5.

What is the least common multiple of $5\left(x+4\right)$ and $\left(x^2-16\right)$ ?

a)

$5\left(x-4\right)\left(x+4\right)$

b)

$5\left(x+4\right)$

c)

$\left(x+4\right)\left(x-4\right)$

d)

$\left(x+4\right)$

6.

What is the least common multiple of $\left(18x-12\right)$ and $\left(6x-4\right)$ ?

a)

$2\left(3x-2\right)$

b)

$6\left(3x-2\right)$

c)

$\left(3x-2\right)$

d)

$\left(18x-12\right)\left(6x-4\right)$

7.

What is the least common multiple of $\left(x^2-6x-16\right)$ and $4\left(x+2\right)$ ?

a)

$\left(x+2\right)$

b)

$4\left(x+2\right)$

c)

$4\left(x-8\right)$

d)

$4\left(x+2\right)\left(x-8\right)$

8.

What is the least common multiple of $\left(x^2-8x+15\right)$ and $\left(6x-18\right)$ ?

a)

$6\left(x-3\right)$

b)

$\left(x-3\right)\left(x-5\right)$

c)

$6\left(x-3\right)\left(x-5\right)$

d)

$\left(x-3\right)$

9.

Rewrite $\frac{4}{3x}$ with a denominator of $12x^2$

a)

$\frac{4}{12x^2}$

b)

$\frac{4x}{12x^2}$

c)

$\frac{16}{12x^2}$

d)

$\frac{16x}{12x^2}$

10.

Rewrite $\frac{x}{2\left(x-1\right)}$ with a denominator of $2\left(x-1\right)\left(x+2\right)$

a)

$\frac{x}{2\left(x-1\right)\left(x+2\right)}$

b)

$\frac{x+2}{2\left(x-1\right)\left(x+2\right)}$

c)

$\frac{x^2+2x}{2\left(x-1\right)\left(x+2\right)}$

d)

$\frac{x^2+2}{2\left(x-1\right)\left(x+2\right)}$

11.

Rewrite $\frac{x+3}{2x+1}$ with a denominator of $\left(x-3\right)\left(2x+1\right)$

a)

$\frac{x+3}{\left(x-3\right)\left(2x+1\right)}$

b)

$\frac{x^2-9}{\left(x-3\right)\left(2x+1\right)}$

c)

$\frac{x-3}{\left(x-3\right)\left(2x+1\right)}$

d)

$\frac{x^2-6x-9}{\left(x-3\right)\left(2x+1\right)}$

12.

Rewrite $\frac{5x}{\left(x^2-4\right)}$ with a denominator of $4x\left(x-2\right)\left(x+2\right)$

a)

$\frac{5x}{4x\left(x-2\right)\left(x+2\right)}$

b)

$\frac{20x}{4x\left(x-2\right)\left(x+2\right)}$

c)

$\frac{20x^2}{4x\left(x-2\right)\left(x+2\right)}$

d)

$\frac{4x^2}{4x\left(x-2\right)\left(x+2\right)}$

13.

Simplify: $\frac{4x-1}{6x}+\frac{5x+7}{6x}$

a)

$\frac{3x+2}{2x}$

b)

$\frac{3x+6}{2x}$

c)

$\frac{9x+1}{x}$

d)

$\frac{9x+6}{6x}$

14.

Simplify: $\frac{4x-1}{2x-5}-\frac{6x+1}{2x-5}$

a)

$\frac{-2x}{2x-5}$

b)

$\frac{-2x-2}{2x-5}$

c)

$\frac{10x}{2x-5}$

d)

$\frac{10x-2}{2x-5}$

15.

Simplify: $\frac{2}{3\left(x+2\right)}-\frac{x}{x\left(x+2\right)}$

a)

$\frac{2-x}{3x\left(x+2\right)}$

b)

$\frac{2-3x}{3x\left(x+2\right)}$

c)

$\frac{x}{3x\left(x+2\right)}$

d)

$\frac{-x}{3x\left(x+2\right)}$

16.

Simplify: $\frac{6x}{x^2-1}+\frac{3}{2\left(x+1\right)}$

a)

$\frac{6x+3}{2\left(x+1\right)\left(x-1\right)}$

b)

$\frac{15x-3}{2\left(x+1\right)\left(x-1\right)}$

c)

$\frac{12x+3}{2\left(x+1\right)\left(x-1\right)}$

d)

$\frac{9x-3}{2\left(x+1\right)\left(x-1\right)}$

17.

Simplify: $\frac{3}{x^2+2x-15}-\frac{1}{6x-18}$

a)

$\frac{-x+8}{6\left(x+5\right)\left(x-3\right)}$

b)

$\frac{-x-2}{6\left(x+5\right)\left(x-3\right)}$

c)

$\frac{-x+23}{6\left(x+5\right)\left(x-3\right)}$

d)

$\frac{-x+13}{6\left(x+5\right)\left(x-3\right)}$

18.

Simplify: $\frac{x}{x^2+3x-4}+\frac{x+1}{x^2-16}$

a)

$\frac{2x^2-5}{\left(x+4\right)\left(x-1\right)\left(x-4\right)}$

b)

$\frac{x^2+x-5}{\left(x+4\right)\left(x-1\right)\left(x-4\right)}$

c)

$\frac{2x^2-4x-1}{\left(x+4\right)\left(x-1\right)\left(x-4\right)}$

d)

$\frac{2x+1}{\left(x+4\right)\left(x-1\right)\left(x-4\right)}$

19.

Simplify

a)

A. $\frac{4x^3}{\left(x+2\right)}$

b)

B. $\frac{4x³}{(x+10)}$

c)

C. $\frac{2x³}{(5x+1)}$

d)

D. $\frac{4x^3}{\left(x-2\right)}$

20.

$\ \frac{5a^3c^{10}}{20a^5c^4}$

a)

$\frac{4c^6}{a^2}$

b)

$\frac{1a^2c^6}{4}$

c)

$\frac{1c^6}{4a^2}$

d)

$\frac{1a^2}{4c^6}$

21.

Simplify.

a)

3 x y³

b)

8 x³ y

c)

3 x³y

d)

8 x y³

22.

Simplify.

a)

$x-3$

b)

$-21$

c)

$-3$

d)

$\frac{x-3}{x}$

23.

Simplify. $\ \frac{x^8y^{12}}{x^4y^{15}}$

a)

$\frac{x^4}{y^3}$

b)

$\frac{x^{12}}{y^3}$

c)

$x^{12}y^{27}$

d)

$\frac{y^3}{x^4}$

24.

Simplify.

a)

1

b)

-1

c)

Can't be simplified

25.

Simplify

a)

$\frac{x+9}{x-9}$

b)

$\frac{1}{(x-9)}$

c)

$x-9$

d)

$\frac{1}{(x+9)}$

e)

$x+9$

26.

Simplify.

a)

$\frac{1}{n-7}$

b)

$n-7$

c)

$\frac{(n-6)}{(n-7)}$

d)

$n-6$

27.

What is the simplified form of the given rational expression?

\frac{x^2-4}{x^2-4x+4}

a)

$\frac{x+2}{x-2}$

b)

$\frac{x-2}{x-2}$

c)

$\frac{x+2}{x+2}$

d)

$1$

e)

$\frac{x-4}{x+4}$

28.

Simplify: $\frac{y^4+3y^3+2y^2}{2y^3-4y^2-16y}$

a)

$\frac{y+1}{y-4}$

b)

$\frac{y+1}{2\left(y-4\right)}$

c)

$\frac{y\left(y+1\right)}{2\left(y-4\right)}$

d)

$\frac{y\left(y+1\right)}{y-4}$

29.

Simplify: $\frac{x^3+3x^2-18x}{x^2+x-12}$

a)

$\frac{x+6}{x+4}$

b)

$\frac{x\left(x+6\right)}{x+4}$

c)

$x^2+6$

d)

$\frac{x\left(x-3\right)}{x-2}$

30.

Simplify: $\frac{14xy^2z^3}{21w^4x^2yz}\cdot\frac{7wxyz}{12w^2y^3z}$

a)

$\frac{7x^2}{9w^5y}$

b)

$\frac{7z^2}{18w^5y}$

c)

$\frac{7wyz^2}{9w^2x^2y^2}$

d)

$\frac{7}{18w^7x^3y^7z^6}$

31.

Simplify: $\frac{x^2-16}{3x^3+18x^2+24x}\cdot\frac{x^3-4x}{2x^2-7x-4}$

a)

$\frac{x-2}{x+1}$

b)

$\frac{x-2}{3\left(2x+1\right)}$

c)

$\frac{3\left(x-2\right)}{2x+1}$

d)

$\frac{x-2}{2x+1}$

32.

Simplify: $\frac{x^2-9}{x^2-4x-21}\div\frac{2x^2+7x+3}{2x^2-15x+7}$

a)

$1$

b)

$\frac{2x-1}{2x+1}$

c)

$\frac{x-3}{x+3}$

d)

$\frac{\left(x-3\right)\left(2x-1\right)}{\left(x+3\right)\left(2x+1\right)}$

33.

Simplify: $\frac{x^2+4x-32}{2x^2+9x-5}\cdot\frac{3x^2-75}{3x^2-11x-4}\div\frac{6x^2-18x-60}{x^3-4x}$

a)

$\frac{x\left(x-2\right)\left(x+8\right)}{2\left(2x-1\right)\left(3x+1\right)}$

b)

$\frac{x\left(x+8\right)}{2\left(3x+1\right)}$

c)

$\frac{2x\left(x+8\right)}{3x+1}$

d)

$\frac{\left(x-2\right)\left(x+8\right)}{\left(2x-1\right)\left(3x+1\right)}$

34.

The first thing that I need to add or subtract fraction is

a)

Have the same numerator

b)

Have the same exact fraction

c)

Have the same denominator

d)

All of the above

35.

Add

a)

b)

c)

d)

36.

a)

b)

c)

d)

37.

Simplify the expression.

a)

b)

c)

d)

38.

Simplify the expression.

a)

b)

c)

d)

39.

Perform the indicated operation and simplify: $\frac{1}{x}-\frac{1}{x-3}$

a)

$\frac{2x-3}{x\left(x-3\right)}$

b)

$\frac{1}{3}$

c)

$\frac{1}{x^2}$

d)

$\frac{-3}{x\left(x-3\right)}$

40.

Perform the indicated operation and simplify: $\frac{x^2+5x-34}{x^2-9x+8}-\frac{10}{x-8}$

a)

$\frac{x^2-5x-44}{\left(x-8\right)\left(x-1\right)}$

b)

$\frac{x^2-5x-24}{\left(x-8\right)\left(x-1\right)}$

c)

$\frac{x+6}{x-1}$

d)

$\frac{x+3}{x-1}$

41.

What would be the common denominator for this expression?

a)

$2x^2$

b)

$2x$

c)

$2x+1$

d)

Doesn't exist

42.

What would be the common denominator for this expression?

a)

$3a$

b)

$2$

c)

$6a$

d)

$5a$

43.

What would be the common denominator for this rational expression?

a)

$z$

b)

$z\left(z+2\right)$

c)

$z^2+2$

d)

$z^2$

44.

Simplify $\frac{x}{x^2-49}-\frac{7}{x^2-49}$

a)

$\frac{7}{x+7}$

b)

$\frac{1}{x-7}$

c)

$\frac{x+7}{x}$

d)

$\frac{1}{x+7}$

45.

To simplify a rational expression, I should

a)

Eliminate common terms in the numerator and denominator.

b)

Combine like terms in the numerator and denominator.

c)

Factor the numerator and denominator and eliminate common factors.

d)

Find an LCD.

46.

Put the numerator and denomenator in parenteses if it has more than one term. For example 3x/(x-1)

(a)

47.

a)

$\frac{2x+12}{x+8}$

b)

$\frac{x+6}{x+4}$

c)

$\frac{x+6}{x+8}$

d)

$\frac{x+3}{x+8}$

48.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

2

b)

18/5

c)

26/5

d)

6

49.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

50.

Solve for x: $\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

51.

Solve: $\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}$

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

52.

Solve $\frac{x-2}{3x}=\frac{1}{3x}+2$

a)

0

b)

$-\frac{3}{5}$

c)

-2

d)

$-\frac{1}{5}$

53.

Solve for y $\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}$

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

54.

$\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}$

a)

$-\frac{23}{5}$

b)

$7$

c)

$-4$

d)

$\frac{4}{3}$

55.

$\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}$

a)

$-2$

b)

$5$

c)

$6$

d)

$\frac{61}{3}$

56.

$\frac{1}{a+1}=\frac{4a+12}{a^2+a}+\frac{1}{a}$

a)

$-\frac{13}{4}$

b)

$-7,\ 1$

c)

$-1$

d)

$7$

57.

$\frac{5}{k+7}=\frac{1}{k+3}+\frac{2k-2}{k^2+10k+21}$

a)

$2$

b)

$1$

c)

$-5$

d)

$5$

58.

$\frac{1}{x+3}=\frac{3}{x+2}-\frac{7}{x^2+5x+6}$

a)

5

b)

$0$

c)

$8$

d)

$3$

59.

a)

x = 2

b)

x = 3/4

c)

x = 4

d)

x = 1/2

PCC Chapter 11 Review

Total questions: 59

Worksheet time: 3hrs 26mins

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