Algebraic Fractions

Adding

100

x / 10 + 2x / 5 

x / 2

200

w / 3 + w / 2

5w / 6

300

(a+1) / 2 + a / 5

(7a + 5) / 10 

400

(m + 5) / m + (m - 2) / 3m 

(4m + 13) / 3m 

500

p / (p-2) + 3 / (p+2) 

(p² + 5p - 6) / (p² - 4) 

Subtracting

100

4m / 5 - m / 15 

11m / 15

200

m / 5 - m / 7 

2m / 35

300

(h-2) / 3 - h / 4

(h-8) / 12

400

(j-5) / 4 - (j-2) / 6 

(j-11) / 12

500

b / (b-2) - 3 / b

(b² - 3b + 6) / (b² - 2b) 

Dividing

100

a / 4 divided by a / 6

3 / 2

200

2r / 9m divided by 4r / 3

1 / 6m 

300

(3+k) / k divided by (k-2) / 15 

(45 + 15k) / (k² - 2k)

400

3ab / 7 divided by 9b² / 14

2a / 3b

500

(2+m) / m divided by (3-m) / m²

(2m + m²) / (3-m) 

Multiplying

100

3m / 5  X  10 / 6m²

1 / m

200

5n / 6 X 3 / 10n

1 / 4

300

ab / (2-a) X (a-2) / a²b

- (1 / a)

400

m / (n+2) X (n+2) / m 

1

500

2x(x²-4)  /  6(x+2) X (x-2) / x

x²-4x+4 / 3

Solving

100

a / 3 = 2

a = 6

200

( 2m / 5 )+ 3 = 4 

m = 5/2

300

(x-2) / 5 - (x-1) / 3 = 1

x = -8

400

5 / 2x - 4/3x = 2 

x = 7 / 12

500

3 / (x+1) = 2 / (x+4) 

x = -10