1) State any restrictions on the variables: 2 y + 1 3 y + 5 y + 4 3 y \frac{2y+1}{3y}+\frac{5y+4}{3y} 3 y 2 y + 1 + 3 y 5 y + 4

y ≠ 0 , − 1 2 , − 4 5 y\ne0,-\frac{1}{2},-\frac{4}{5} y  = 0 , − 2 1 , − 5 4

y ≠ − 3 y\ne-3 y  = − 3

N o r e s t r i c t i o n s No\ restrictions N o r e s t r i c t i o n s

2) State any restrictions on the variables: 5 n 30 m + 2 m + 4 n 30 m \frac{5n}{30m}+\frac{2m+4n}{30m} 3 0 m 5 n + 3 0 m 2 m + 4 n

m ≠ 0 a n d n ≠ 0 m\ne0\ and\ n\ne0 m  = 0 a n d n  = 0

N o r e s t r i c t i o n s No\ restrictions N o r e s t r i c t i o n s

7) Simplify each expression: b − 3 12 b + 18 + 4 b 12 b + 18 \frac{b-3}{12b+18}+\frac{4b}{12b+18} 1 2 b + 1 8 b − 3 + 1 2 b + 1 8 4 b

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

1 7 b + 15 \frac{1}{7b+15} 7 b + 1 5 1

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

7) State any restrictions on the variables: b − 3 12 b + 18 + 4 b 12 b + 18 \frac{b-3}{12b+18}+\frac{4b}{12b+18} 1 2 b + 1 8 b − 3 + 1 2 b + 1 8 4 b

b ≠ − 3 2 b\ne-\frac{3}{2} b  = − 2 3

b ≠ 0 , − 18 b\ne0,-18 b  = 0 , − 1 8

b ≠ 3 5 b\ne\frac{3}{5} b  = 5 3

b ≠ − 12 b\ne-12 b  = − 1 2

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

v ≠ 2 5 v\ne\frac{2}{5} v  = 5 2

v ≠ − 8 v\ne-8 v  = − 8

v ≠ − 8 , 2 5 v\ne-8,\frac{2}{5} v  = − 8 , 5 2

v ≠ 0 , 1 2 , 2 5 v\ne0,\frac{1}{2},\frac{2}{5} v  = 0 , 2 1 , 5 2

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

− 3 ( n + 19 ) ( n + 7 ) ( n − 2 ) \frac{-3\left(n+19\right)}{\left(n+7\right)\left(n-2\right)} ( n + 7 ) ( n − 2 ) − 3 ( n + 1 9 )

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

− 3 n + 41 ( n + 7 ) ( n − 2 ) \frac{-3n+41}{\left(n+7\right)\left(n-2\right)} ( n + 7 ) ( n − 2 ) − 3 n + 4 1

− 3 n + 5 \frac{-3}{n+5} n + 5 − 3

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

n ≠ − 7 , 2 n\ne-7,2 n  = − 7 , 2

n ≠ − 7 , 0 , 2 n\ne-7,0,2 n  = − 7 , 0 , 2

n ≠ − 3 , − 7 , 2 n\ne-3,-7,2 n  = − 3 , − 7 , 2

n ≠ − 7 , − 4 , 2 n\ne-7,-4,\ 2 n  = − 7 , − 4 , 2

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

x ≠ − 1 2 , − 3 x\ne-\frac{1}{2},-3 x  = − 2 1 , − 3

x ≠ − 1 2 , − 2 , − 3 x\ne-\frac{1}{2},-2,-3 x  = − 2 1 , − 2 , − 3

x ≠ 0 , ± 1 2 , − 3 x\ne0,\pm\frac{1}{2},-3 x  = 0 , ± 2 1 , − 3

x ≠ 0 , − 3 , − 1 2 x\ne0,-3,-\frac{1}{2} x  = 0 , − 3 , − 2 1

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

v ≠ − 6 , 3 v\ne-6,3 v  = − 6 , 3

v ≠ − 3 , 6 v\ne-3,6 v  = − 3 , 6

v ≠ − 3 , − 6 v\ne-3,-6 v  = − 3 , − 6

v ≠ 3 , 6 v\ne3,6 v  = 3 , 6

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

12 x ( x + 3 ) ( x + 6 ) \frac{12x}{\left(x+3\right)\left(x+6\right)} ( x + 3 ) ( x + 6 ) 1 2 x

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

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

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

x ≠ − 3 , − 6 x\ne-3,-6 x  = − 3 , − 6

x ≠ 3 , − 6 x\ne3,-6 x  = 3 , − 6

x ≠ − 3 , 6 x\ne-3,6 x  = − 3 , 6

x ≠ 3 , 6 x\ne3,6 x  = 3 , 6

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

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

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

12 x − 1 \frac{12}{x-1} x − 1 1 2

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

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

x ≠ − 1 , 2 x\ne-1,2 x  = − 1 , 2

x ≠ − 1 , 2 , − 6 x\ne-1,2,-6 x  = − 1 , 2 , − 6

x ≠ 1 , − 2 x\ne1,-2 x  = 1 , − 2

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

x ≠ 0 , 5 x\ne0,5 x  = 0 , 5

x ≠ 0 , 3 , 5 x\ne0,3,5 x  = 0 , 3 , 5

x ≠ − 4 , 0 , 3 , 5 x\ne-4,0,3,5 x  = − 4 , 0 , 3 , 5

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

x ≠ − 1 , 2 x\ne-1,2 x  = − 1 , 2

x ≠ ± 1 , ± 2 x\ne\pm1,\pm2 x  = ± 1 , ± 2

x ≠ − 2 , 1 x\ne-2,1 x  = − 2 , 1

x ≠ − 2 , − 1 x\ne-2,-1 x  = − 2 , − 1

8.5A Adding/Subtracting Rational Expressions Worksheet

Authored by Shari McCourt

Mathematics

11th - 12th Grade

CCSS covered

Used 77+ times

8.5A Adding/Subtracting Rational Expressions Worksheet

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

1) Simplify each expression:
$\frac{2y+1}{3y}+\frac{5y+4}{3y}$

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

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

$4y+5$

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

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

1) State any restrictions on the variables:
$\frac{2y+1}{3y}+\frac{5y+4}{3y}$

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

$y\ne-3$

$No\ restrictions$

$y\ne0$

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

2) Simplify each expression:
$\frac{5n}{30m}+\frac{2m+4n}{30m}$

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

$\frac{3m}{5}$

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

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

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

2) State any restrictions on the variables:
$\frac{5n}{30m}+\frac{2m+4n}{30m}$

$m\ne0$

$n\ne0$

$m\ne0\ and\ n\ne0$

$No\ restrictions$

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

3) Simplify each expression:
$\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}$

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

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

$-v$

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

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

3) State any restrictions on the variables:
$\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}$

$u\ne0\ and\ v\ne0$

$No\ restrictions$

$u\ne0$

$v\ne0$

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

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

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

$\frac{3}{y}$

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

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

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

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

$y\ne0$

$y\ne\pm3$

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

$\frac{5}{11a}$

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

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

$\frac{2}{3a}$

Tags

CCSS.HSA.APR.D.7

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

$a\ne-6,-30$

$a\ne0$

$a\ne\pm5$

$a\ne0,-5$

Tags

CCSS.HSA.APR.D.7

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8.5A Adding/Subtracting Rational Expressions Worksheet

1) Simplify each expression: 2y+13y+5y+43y\frac{2y+1}{3y}+\frac{5y+4}{3y}3y2y+1​+3y5y+4​

1) State any restrictions on the variables: 2y+13y+5y+43y\frac{2y+1}{3y}+\frac{5y+4}{3y}3y2y+1​+3y5y+4​

2) Simplify each expression: 5n30m+2m+4n30m\frac{5n}{30m}+\frac{2m+4n}{30m}30m5n​+30m2m+4n​

2) State any restrictions on the variables: 5n30m+2m+4n30m\frac{5n}{30m}+\frac{2m+4n}{30m}30m5n​+30m2m+4n​

3) Simplify each expression: u+5v8v2u2−u−6v8v2u2\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}8v2u2u+5v​−8v2u2u−6v​

3) State any restrictions on the variables: u+5v8v2u2−u−6v8v2u2\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}8v2u2u+5v​−8v2u2u−6v​

4) Simplify each expression: 6y−49y2−1+3y+19y2−1\frac{6y-4}{9y^2-1}+\frac{3y+1}{9y^2-1}9y2−16y−4​+9y2−13y+1​

4) State any restrictions on the variables: 6y−49y2−1+3y+19y2−1\frac{6y-4}{9y^2-1}+\frac{3y+1}{9y^2-1}9y2−16y−4​+9y2−13y+1​

5) Simplify each expression: 4a−56a2+30a+a−16a2+30a\frac{4a-5}{6a^2+30a}+\frac{a-1}{6a^2+30a}6a2+30a4a−5​+6a2+30aa−1​

5) State any restrictions on the variables: 4a−56a2+30a+a−16a2+30a\frac{4a-5}{6a^2+30a}+\frac{a-1}{6a^2+30a}6a2+30a4a−5​+6a2+30aa−1​

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1) Simplify each expression:
$\frac{2y+1}{3y}+\frac{5y+4}{3y}$

1) State any restrictions on the variables:
$\frac{2y+1}{3y}+\frac{5y+4}{3y}$

2) Simplify each expression:
$\frac{5n}{30m}+\frac{2m+4n}{30m}$

2) State any restrictions on the variables:
$\frac{5n}{30m}+\frac{2m+4n}{30m}$

3) Simplify each expression:
$\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}$

3) State any restrictions on the variables:
$\frac{u+5v}{8v^2u^2}-\frac{u-6v}{8v^2u^2}$

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

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

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

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