Free Printable LAS #1.8: OPERATIONS ON RATIONAL ALGEBRAIC EXPRESSIONS

1.

Find the product: $\frac{a+b}{a^3+b^3}\times\frac{a^2-ab+b^2}{a-b}$

a)

$\frac{a+b}{a^2-b^2}$

b)

$\frac{1}{a-b}$

c)

$a+b$

d)

1

2.

Find the quotient: $\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}$

a)

$\frac{5a\left(a+4\right)}{3}$

b)

$\frac{a^3-2a^2-4a+8}{15a^3}$

c)

$\frac{5a^2+20a}{3}$

d)

$\frac{a^3-6a+8}{15a}$

3.

Subtract: $\frac{9x+1}{x-2}-\frac{3x-4}{x-2}$

a)

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

b)

$\frac{12x+5}{x-2}$

c)

$\frac{6x+5}{x-2}$

d)

$\frac{12x-3}{x-2}$

4.

Find the sum: $\frac{x}{x+1}+\frac{2x}{x+2}$

a)

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

b)

$\frac{3x^2+4x}{\left(x+1\right)\left(x+23\right)}$

c)

$\frac{3x}{\left(x+1\right)\left(x+23\right)}$

d)

$\frac{3x^2+4x}{\left(x+1\right)\left(x+2\right)}$

5.

Multiply

\frac{9c}{9c^2-1}.\ \frac{3c-1}{3c}

a)

$\frac{3}{3c+1}$

b)

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

c)

$\frac{3c}{3c+1}$

d)

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

6.

Multiply $\frac{\left(x^2+10x+25\right)}{\left(x+6\right)}.\ \frac{\left(x^2+12x+36\right)}{\left(x+5\right)}$

a)

(x+5)(x+5)

b)

(x+6)(x+6)

c)

(X+5)(x+6)

d)

(x+5)(x+6)(x+5)

7.

$Divide\ \frac{\left(m-2\right)}{3m}\div\frac{\left(m^2-4\right)}{6m^2}$

a)

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

b)

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

c)

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

d)

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

8.

$Find\ the\ LCD\ of\ \frac{x}{\left(x^2-9\right)}\ +\frac{2x}{\left(x^2+6x+9\right)}$

a)

(x+3)(x3)(x-3)

b)

(x+3)(x-3)

c)

(x+3)(x+3)

d)

(x+3)(x-3)(x+2)

9.

$Add\ \frac{4y-3}{y+2}+\frac{5-3y}{y+2}$

a)

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

b)

$\frac{2}{y+2}$

c)

y+2

d)

1

10.

$Subract\ \frac{x+9}{x+3}-\frac{-4x\ -5}{x+3}$

a)

$\frac{5x+15}{x+3}$

b)

$5$

c)

$\frac{5x+3}{x+3}$

d)

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

11.

$Add\frac{x+y}{xy^2}+\frac{3x+y}{x^2y}$

a)

$\frac{x^2+4xy+y^2}{x^2y^2}$

b)

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

c)

$\frac{x^2+2xy+y^2}{xy}$

d)

$\frac{x^2+y^2}{xy}$

12.

$\frac{3x\ +\ 4}{x^2\ -\ 16}\ -\ \frac{2x}{x^2-16}=$

a)

$1$

b)

$\frac{x+4}{x^2-16}$

c)

$\frac{1}{x-4}$

d)

$\frac{1}{x+4}$

13.

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

a)

$x^2$

b)

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

c)

1

d)

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

14.

Find the difference: $\frac{2x-1}{y}-\frac{5x+8}{y}$ .

a)

$\frac{3x+9}{y}$

b)

$\frac{-3x+9}{y}$

c)

$\frac{3x-9}{y}$

d)

$\frac{-3x-9}{y}$

15.

What is the product of $\frac{10x^2}{3y^3}\cdot\frac{9y^2}{15x^2}$ ?

a)

$\frac{2}{y}$

b)

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

c)

$\frac{y}{2}$

d)

$\frac{2x}{y}$

16.

Find the quotient: $\frac{14b^7}{5c^5}\div\frac{7b^3}{20c^2}$ .

a)

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

b)

$\frac{8b^4}{c^3}$

c)

$\frac{10b^4}{c^4}$

d)

$\frac{12b^4}{c^5}$

17.

What is the difference if $\frac{10}{x-3}$ is subtracted from $\frac{2x+9}{x-3}$ ?

a)

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

b)

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

c)

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

d)

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

18.

Find the product.

\frac{𝑥^2−9}{4𝑥+12}\ •\ \ \frac{8}{x^2-6x+9}\ =

a)

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

b)

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

c)

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

d)

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

19.

Divide:

\frac{2x-12}{x+5}\div\frac{x-6}{x+5\ }=

a)

$2x-12$

b)

$\frac{2x^2-12x}{x-6}$

c)

$\frac{1}{2}$

d)

$2$

20.

Divide:

\frac{x^2+x}{x-1}\div\frac{x^2}{x^2-1}

a)

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

b)

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

c)

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

d)

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

LAS #1.8: OPERATIONS ON RATIONAL ALGEBRAIC EXPRESSIONS

Total questions: 20

Worksheet time: 2hrs 50mins

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