Free Printable Test 10 Review: Rational Expressions (22-23)

1.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

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

b)

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

c)

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

d)

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

2.

Simplify

a)

A.(x+7)/(x-4)

b)

B.-3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

3.

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

a)

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

b)

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

c)

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

d)

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

4.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

5.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

6.

$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$

a)

$\frac{x+5}{x-1}$

b)

$\frac{x-5}{x-1}$

c)

$\frac{x+5}{x+1}$

d)

$\frac{x-5}{x+1}$

7.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

8.

a)

b)

c)

d)

9.

Simplify $\frac{7n}{3n-18}+\frac{n+3}{3}$

a)

$\frac{8n+3}{3n-15}$

b)

$\frac{n^2+4n-18}{3\left(n-6\right)}$

c)

$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$

d)

$\frac{7n+n+3}{3n-18+3}$

10.

Simplify $\frac{8n}{n-3}+\frac{3n}{5n-6}$

a)

$\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$

b)

$\frac{11n}{6n-9}$

c)

$\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$

d)

$\frac{8n+3n}{n-3+5n-6}$

11.

$2-\frac{7}{x^2+x-30}$ Simplify

a)

$\frac{2x^2-2x-67}{\left(x-6\right)\left(x+5\right)}$

b)

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

c)

$\frac{-5}{x^2+x-30}$

d)

$\frac{2x^2+2x-67}{\left(x+6\right)\left(x-5\right)}$

12.

$\frac{4x}{x-5}-\frac{3}{x-6}$ Simplify

a)

$\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$

b)

$\frac{4x-3}{2x+1}$

c)

$\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}$

d)

$\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}$

13.

Simplify $\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}$

a)

$\frac{n-3}{n-8}$

b)

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

c)

$\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}$

d)

$\frac{n^2+2n-14}{2n-3}$

14.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

15.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

16.

a)

5x / 3

b)

10x / (x - 8)

c)

10x

d)

6x(x - 8) / 6x

17.

a)

(x + 9)

b)

(x - 3) / (x + 2)

c)

(x + 9) / (x + 2)

d)

(x - 3)

18.

a)

n - 1

b)

2(n - 1) / 2

c)

2(n - 1)

d)

1

19.

$\frac{2a-20}{6a}\times\frac{a-9}{a-10}$ Simplify

a)

$\frac{2a^2-180}{6a^2-60a}$

b)

$\frac{2\left(a-9\right)}{6a}$

c)

$\frac{a-9}{3a}$

d)

$\frac{3a-29}{7a-10}$

20.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

21.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

22.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

23.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

24.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

25.

$\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}$ Simplify

a)

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

b)

$\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}$

c)

$\frac{m^2+2m-32}{m^2+14m+49}$

d)

$\frac{-5}{2m^2}$

26.

$\frac{3x+2}{x+2}\div x-1$

a)

$3\left(x-1\right)$

b)

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

c)

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

d)

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

27.

$\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}$

a)

$\frac{2}{m-64m^2}$

b)

$\frac{16m^2}{8m^2\left(m-8\right)}$

c)

$\frac{2}{64m^4\left(m-8\right)}$

d)

$\frac{2}{m-8}$

28.

Simplify.
$\frac{\frac{3x+2}{x^2}-\frac{3}{x^2}}{\frac{3x+2}{x^2}-\frac{3}{2}}$

a)

$\frac{6x-2}{6x+4-3x^2}$

b)

$\frac{29x^2+36x+12+3x^3}{27x^2+9x^5+12x^4+4x^3}$

c)

$\frac{18x^2+8x}{24+9x}$

d)

$\frac{-45x-30}{-12x-36x^2-16}$

29.

Simplify.
$\frac{\frac{1}{x}}{\frac{x-1}{16}}$

a)

$\frac{1}{x}$

b)

$\frac{16x-16}{x^3}$

c)

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

d)

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

30.

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

a)

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

b)

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

c)

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

d)

$\frac{1}{x}$

31.

$\frac{\frac{x}{25}+\frac{x}{5}}{\frac{5}{x}}$

a)

$\frac{25x^2}{400+4x}$

b)

$\frac{6x^2}{125}$

c)

$\frac{400x}{x^3-16}$

d)

$\frac{x^2+x^3}{625}$

32.

$\frac{m}{\frac{1}{3}+\frac{18}{m}}$ Simplify

a)

$\frac{3m^2}{m+54}$

b)

$\frac{m}{\frac{m+54}{3m}}$

c)

$\frac{3}{m+54}$

d)

$\frac{3m^2}{19}$

33.

Bob has factored the denominators and made sure there is a common denominator. He must be...

a)

Adding or Subtracting Rational Expressions

b)

Multiplying Rational Expressions

c)

Dividing Rational Expressions

34.

Simplify the expression.

a)

b)

c)

d)

35.

Add

a)

A.

b)

B.

c)

C.

d)

D.

36.

What is the LCM of:

24p^7q,\ \ 30p^2q^2,\ \ \ 45pq^3

?

a)

$120p^7q^2$

b)

$45pq$

c)

$360pq$

d)

$360p^7q^3$

37.

What is the LCM for the polynomials given in factored form:

\left(x+2\right)\left(x-3\right),\ \ \ \left(x-5\right)\left(x-3\right)

a)

$\left(x-3\right)$

b)

$\left(x+2\right)\left(x-3\right)\left(x-5\right)$

c)

$\left(x+2\right)\left(x-5\right)$

d)

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

38.

Add:

\frac{3x}{5a}+\frac{7y}{5a}

a)

$\frac{3x+7y}{5a}$

b)

$\frac{10xy}{10a^2}$

c)

$\frac{10xy}{5a}$

d)

$\frac{3x+7y}{5a^2}$

39.

What should be the new numerator to replace the ? below when adding the given fractions?

$\frac{2}{3x}+\frac{5}{7y}$

\ \ \ \updownarrow\ \ \ \ \ \ \ \ \ \updownarrow

\frac{14y}{21xy}+\frac{?}{21xy}

a)

$15x$

b)

$35y$

c)

$5x$

d)

$15xy$

40.

Add:

$\frac{2}{x+3}+\frac{1}{x}$

a)

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

b)

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

c)

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

d)

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

41.

Subtract:
$\frac{5x-3}{x+2}-\frac{3x-1}{x+2}$

a)

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

b)

$\frac{8x-4}{x+2}$

c)

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

d)

$\frac{2x-2}{0}$

42.

Add:
$\frac{5}{x-2}+\frac{3}{x+7}$

a)

$\frac{8}{\left(x-2\right)\left(x+7\right)}$

b)

$\frac{8}{2x+5}$

c)

$\frac{8x}{\left(x-2\right)\left(x+7\right)}$

d)

$\frac{8x+29}{\left(x-2\right)\left(x+7\right)}$

43.

What is/are the restricted value(s) of the expression?

a)

x ≠ 2

b)

x ≠ -1

c)

x ≠ 2

x ≠ -1

d)

x ≠ -2

x ≠ 1

44.

Simply the expression. State the restricted values.

a)

b)

c)

d)

_{Restricted values: 4, 10}

e)

Restricted values: -4, -10

45.

Simply the expression. State the restricted values.

a)

b)

c)

d)

Restricted values: 5, -5

e)

Restricted values: 0, 5

46.

Simply the expression. State the restricted values.

a)

b)

c)

d)

Restricted Values: -4, -5

e)

Restricted Values: 2, -4

47.

Simply the the expression. State the restricted values.

a)

b)

c)

d)

Restricted values: 0, -1/5

e)

Restricted values: 0, 1/5

48.

Simply the expression. State the restricted values.

a)

b)

c)

d)

Restricted values: 1, 2/5

e)

Restricted values: -1, 5/2

49.

Simply the expression. State the restricted values.

a)

b)

c)

d)

Restricted Values: 1, -3/2

e)

Restricted Values: -1, 3/2

50.

Simply the expression. State the restricted values.

a)

b)

c)

d)

Restricted values: 3

e)

Restricted values: -2, -3

51.

Simply each expression. State the restricted values.

a)

b)

c)

d)

Restricted values: -3, -3/2

e)

Restricted values: 3, -2/3

52.

What are the restricted values?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

53.

Identify the restricted values

a)

x≠-6

b)

x≠-6, 3

c)

x≠3

d)

x≠-18

54.

Find the sum:

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

a)

$\frac{10}{x}$

b)

$\frac{10}{2x}$

c)

$\frac{5}{x}$

d)

$\frac{10}{x^2}$

55.

Find the difference:

\frac{2x}{x^3-2}-\frac{1}{x^3-2}

a)

$\frac{2x-1}{x^3-2}$

b)

$\frac{2x+1}{x^3-2}$

c)

$\frac{2x-1}{2x^3-4}$

d)

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

56.

$\frac{u-v}{8v}+\frac{6u-3v}{8v}$

a)

$\frac{7u-4v}{16v}$

b)

$\frac{7u-4v}{8v}$

c)

$\frac{7u+2v}{8v}$

d)

$\frac{7u+2v}{16v}$

57.

Simplify the expression

a)

6x / 20xy

b)

3 / 10y

c)

(6x+1) / (20xy)

d)

3 / 20xy

58.

Simplify the expression

a)

(2a + 4b) / 12b²

b)

(2a - 4b) / 12b²

c)

(a - b) / 6b²

d)

(a + 2b) / 6b²

Test 10 Review: Rational Expressions (22-23)

Total questions: 58

Worksheet time: 4hrs 48mins

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