Free Printable 8.5A Adding/Subtracting Rational Expressions Worksheet

1.

1) Simplify each expression:

\frac{2y+1}{3y}+\frac{5y+4}{3y}

a)

$\frac{7y+5}{6y}$

b)

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

c)

$4y+5$

d)

$\frac{10y^2+4}{9y^2}$

2.

1) State any restrictions on the variables:

\frac{2y+1}{3y}+\frac{5y+4}{3y}

a)

$y\ne0,-\frac{1}{2},-\frac{4}{5}$

b)

$y\ne-3$

c)

$No\ restrictions$

d)

$y\ne0$

3.

2) Simplify each expression:

\frac{5n}{30m}+\frac{2m+4n}{30m}

a)

$\frac{9n+2m}{60m}$

b)

$\frac{3m}{5}$

c)

$\frac{10mn+20n^2}{900m^2}$

d)

$\frac{9n+2m}{30m}$

4.

2) State any restrictions on the variables:

\frac{5n}{30m}+\frac{2m+4n}{30m}

a)

$m\ne0$

b)

$n\ne0$

c)

$m\ne0\ and\ n\ne0$

d)

$No\ restrictions$

5.

3) Simplify each expression:

\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}

a)

$-\frac{1}{8vu^2}$

b)

$\frac{2u-v}{8v^2u^2}$

c)

$-v$

d)

$\frac{11}{8vu^2}$

6.

3) State any restrictions on the variables:

\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}

a)

$u\ne0\ and\ v\ne0$

b)

$No\ restrictions$

c)

$u\ne0$

d)

$v\ne0$

7.

4) Simplify each expression: $\frac{6y-4}{9y^2-1}+\frac{3y+1}{9y^2-1}$

a)

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

b)

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

c)

$\frac{3}{y}$

d)

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

8.

4) State any restrictions on the variables: $\frac{6y-4}{9y^2-1}+\frac{3y+1}{9y^2-1}$

a)

$y\ne\pm\frac{1}{3}$

b)

$y\ne\frac{1}{9}$

c)

$y\ne0$

d)

$y\ne\pm3$

9.

5) Simplify each expression: $\frac{4a-5}{6a^2+30a}+\frac{a-1}{6a^2+30a}$

a)

$\frac{5}{11a}$

b)

$\frac{5a+4}{6a\left(a+5\right)}$

c)

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

d)

$\frac{2}{3a}$

10.

5) State any restrictions on the variables: $\frac{4a-5}{6a^2+30a}+\frac{a-1}{6a^2+30a}$

a)

$a\ne-6,-30$

b)

$a\ne0$

c)

$a\ne\pm5$

d)

$a\ne0,-5$

11.

6) Simplify each expression: $\frac{5x+4}{9x^3+27x^2}-\frac{x-8}{9x^3+27x^2}$

a)

$\frac{4}{9x^2}$

b)

$\frac{4\left(x-1\right)}{9x^2\left(x+3\right)}$

c)

$\frac{5}{36x^2}$

d)

$\frac{4\left(x-3\right)}{9x^2\left(x+3\right)}$

12.

6) State any restrictions on the variables: $\frac{5x+4}{9x^3+27x^2}-\frac{x-8}{9x^3+27x^2}$

a)

$x\ne0,-3$

b)

$x\ne-9$

c)

$x\ne\pm3$

d)

$x\ne0,1,-3$

13.

7) Simplify each expression: $\frac{b-3}{12b+18}+\frac{4b}{12b+18}$

a)

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

b)

$\frac{1}{2b}$

c)

$\frac{1}{7b+15}$

d)

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

14.

7) State any restrictions on the variables: $\frac{b-3}{12b+18}+\frac{4b}{12b+18}$

a)

$b\ne0,-18$

b)

$b\ne-\frac{3}{2}$

c)

$b\ne\frac{3}{5}$

d)

$b\ne-12$

15.

8) Simplify each expression: $\frac{n-4}{n^2-n-20}+\frac{n+1}{n^2-n-20}$

a)

$\frac{2n-5}{n+4}$

b)

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

c)

$\frac{2n-3}{\left(n-5\right)\left(n+4\right)}$

d)

$\frac{-3}{n^2-20}$

16.

8) State any restrictions on the variables: $\frac{n-4}{n^2-n-20}+\frac{n+1}{n^2-n-20}$

a)

$n\ne\frac{3}{2},5,-4$

b)

$n\ne20$

c)

$n\ne0,\frac{3}{2}$

d)

$n\ne5,\ -4$

17.

9) Simplify each expression: $\frac{7v}{8}-\frac{8v-4}{5v-2}$

a)

$\frac{35v^2+50v-32}{8\left(5v-2\right)}$

b)

$\frac{v+4}{8\left(5v-2\right)}$

c)

$\frac{35v^2-78v+32}{8\left(5v-2\right)}$

d)

$\frac{-\left(v+4\right)}{8\left(5v-2\right)}$

18.

9) State any restrictions on the variables: $\frac{7v}{8}-\frac{8v-4}{5v-2}$

a)

$v\ne-8$

b)

$v\ne-8,\frac{2}{5}$

c)

$v\ne0,\frac{1}{2},\frac{2}{5}$

d)

$v\ne\frac{2}{5}$

19.

10) Simplify each expression: $\frac{4}{n+7}-\frac{7}{n-2}$

a)

$\frac{-3\left(n+19\right)}{\left(n+7\right)\left(n-2\right)}$

b)

$\frac{-3}{\left(n+7\right)\left(n-2\right)}$

c)

$\frac{-3n+41}{\left(n+7\right)\left(n-2\right)}$

d)

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

20.

10) State any restrictions on the variables: $\frac{4}{n+7}-\frac{7}{n-2}$

a)

$n\ne-7,0,2$

b)

$n\ne-3,-7,2$

c)

$n\ne-7,-4,\ 2$

d)

$n\ne-7,2$

21.

11) Simplify each expression: $\frac{2}{x+3}-\frac{6x}{2x+1}$

a)

$\frac{-2\left(3x^2+7x-1\right)}{\left(x+3\right)\left(2x+1\right)}$

b)

$\frac{-\left(6x^2+7x-2\right)}{x+3}$

c)

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

d)

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

22.

11) State any restrictions on the variables: $\frac{2}{x+3}-\frac{6x}{2x+1}$

a)

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

b)

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

c)

$x\ne0,\pm\frac{1}{2},-3$

d)

$x\ne0,-3,-\frac{1}{2}$

23.

12) Simplify each expression: $\frac{5v}{v-3}+\frac{5}{v+6}$

a)

$\frac{5\left(v+1\right)}{\left(v-3\right)\left(v+6\right)}$

b)

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

c)

$\frac{10v}{\left(v-3\right)\left(v+6\right)}$

d)

$\frac{5\left(v^2+7v-3\right)}{\left(v-3\right)\left(v+6\right)}$

24.

12) State any restrictions on the variables: $\frac{5v}{v-3}+\frac{5}{v+6}$

a)

$v\ne-3,6$

b)

$v\ne-6,3$

c)

$v\ne-3,-6$

d)

$v\ne3,6$

25.

13) Simplify each expression: $\frac{4x}{x+3}-\frac{4x}{x+6}$

a)

0

b)

$\frac{12x}{\left(x+3\right)\left(x+6\right)}$

c)

$\frac{36x}{\left(x+3\right)\left(x+6\right)}$

d)

$\frac{4x\left(2x+9\right)}{\left(x+3\right)\left(x+6\right)}$

26.

13) State any restrictions on the variables: $\frac{4x}{x+3}-\frac{4x}{x+6}$

a)

$x\ne3,-6$

b)

$x\ne-3,6$

c)

$x\ne-3,-6$

d)

$x\ne3,6$

27.

14) Simplify each expression: $\frac{6}{x-2}+\frac{6}{x+1}$

a)

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

b)

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

c)

$\frac{12}{x-1}$

d)

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

28.

14) State any restrictions on the variables: $\frac{6}{x-2}+\frac{6}{x+1}$

a)

$x\ne1$

b)

$x\ne-1,2,-6$

c)

$x\ne1,-2$

d)

$x\ne-1,2$

29.

15) Simplify each expression: $\frac{x}{x-5}+\frac{x-3}{4x}$

a)

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

b)

$\frac{-7x+15}{\left(x-5\right)}$

c)

$\frac{2x-3}{4x\left(x-5\right)}$

d)

$\frac{5x^2-8x+15}{4x\left(x-5\right)}$

30.

15) State any restrictions on the variables: $\frac{x}{x-5}+\frac{x-3}{4x}$

a)

$x\ne0,3,5$

b)

$x\ne-4,0,3,5$

c)

$x\ne5$

d)

$x\ne0,5$

31.

16) Simplify each expression: $\frac{x-1}{x-2}+\frac{x+2}{x+1}$

a)

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

b)

$1$

c)

$-1$

d)

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

32.

16) State any restrictions on the variables: $\frac{x-1}{x-2}+\frac{x+2}{x+1}$

a)

$x\ne-1,2$

b)

$x\ne\pm1,\pm2$

c)

$x\ne-2,1$

d)

$x\ne-2,-1$

8.5A Adding/Subtracting Rational Expressions Worksheet

Total questions: 32

Worksheet time: 8hrs 0mins

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