Rational Expressions

Simplifying Rational Expressions

100

(x^2 -9) / (x+3)

x-3

200

(x^2+5x+6)/(x^2 - x - 6)

(x+3)/(x-3)

300

(x^2-4x+4)/(x^2-2x)

(x-2)/x

400

(4a^2-36a)/(2a^4-24a^3+54a^2)

2/(a(a-3))

500

(y^2 - 36)/(5y^2-26y-24)

(y+6)/(5y+4)

Multiplying/Dividing Rational Expressions

100

(28x^3y)/(3xy^2)*(9y)/(7x^2y^4)

12/y^4

200

(28n+40)/(35n+50)* (12n+24)/(8n+16)

6/5

300

(1-h^2)/(2h^2-10h-12) / (2h-2)/6

-3/(2(n-6))

400

(2n-3)/(n+1) * (2n^2 +5n+3)/(9-4n^2)

-1

500

(20x-4)/(8x^2) / (5x-1) * (6x)/5

3/(5x)

Simplifying Rational Expressions with Addition and Subtractions

100

(9w^3)/(2w^5) + (3w^3)/(2w^5)

6/w^2

200

(x^2+5x)/(x+7) - (14)/(x+7)

x-2

300

(v^2-4v)/(5v^2+9v-2) - (2v+16)/(5v^2+9v-2)

(v-8)/(5v-1)

400

(3c)/(c-4) - 2/5

(13c+8)/(5(c-4))

500

r/(r^2-4) + 1/(r^2-6r+8)

(r-1)/((r+2)(r-4))

Complex Fractions

100

((18x^2)/(x-1)/x/(2x-2))

36x

200

(n^2-9n+14)/(4n+28)/(n-7)/(n+7)

(n-2)/4

300

x^2/4/((x^2/4)-4/x)

x^3/(x^3-16)

400

(1-(a/(a-b)))/(1/(a-b)

-b

500

((2/(x+3))-(1/3))/((x^2/3)-3

1/(x+3)^2

Solving Rational Equations

100

5/m=8/(2m-6)

m=15

200

(x+5)/5=6/(x-2)

x=-8, x=5

300

2/(a-2)=(3a-1)/(2a+11)

a=-4/3, a=5

400

x+(10/(x-9))=2

x=4, x=7

500

(y+6)/(y-1) - (y-4)/(y^2-y) = 1/(y-1)

y=-2