Rational Expressions

Simplifying Rational Expressions

100

Simplify.

(x^2 - 81)/(x - 9)

x + 9

200

Simplify.

(x^2 + 10x + 25)/(x + 5)

x + 5

300

Simplify.

(8x^3 -27)/(2x - 3)

2x^2 + 6x + 9

400

Simplify.

(x^2 - 9x + 14)/(x^2 - 49)

(x-2)/(x+7)

500

Simplify.

(3x^3 + 6x^2 + 4x + 8)/(5x^2 - 20)

(3x^2 + 4)/(5(x-2)

Multiplying & Dividing Rational Expressions

100

Multiply.

(x+2)/(4x+8) * (5x+60)/(x+12)

5/4

200

Divide.

(x-3)/(4x-16)/(5x-15)/(8x-32)

2/5

300

Simplify.

7/x^2*(x^2 -49)/(7x-49)/(x^2+13x+42)/(x^3+6x^2)

1

400

Simplify.

(3x+6)/(x-9)/(9x+18)/(7x-63)*(x-1)/(1-x)

-7/3

500

Simplify.

(x^2 +12x+27)/(x^2+6x - 7)/(x^2+16x+63)/(x^2 -13x+12)/(x^2 - 9x - 36)/(2x^2+19x+35)

(2x+5)/(x+7)

Adding & Subtracting Rational Expressions

100

Add.

4/(5v^2x)+3/(4v^3x^2)

(16vx+15)/(20v^3x^2)

200

Add.

(x+4)/(x+2)+(4x-2)/(5x+10)

(9x+18)/(5x+10)

300

Subtract.

(x+5)/(3x+12) - (x-4)/(4x+16)

(x+32)/(12(x+4)

400

Simplify.

2/(y-5) + (8y)/(y^2 - 49)-3/(y-7)

(7y^2 -46y+7)/((y-7)(y+7)(y-5))

500

Simplify and write as a single fraction.

2/(v^2 +15v+56)-4/(v^2 -v-56)+3/(v^2 -64)

(-4v^2 -27v+5)/((v-8)(v+7)(v+8)

Complex Fractions of Rational Expressions

100

Simplify.

((x/4)-(4/x))/((1/4)+(1/x))

x-4

200

Simplify.

(d^-2-c^-2)/(d^-1-c^-1)

(c+d)/(dc)

300

Simplify.

(5/(1+h)-5)/h

-5/(1+h)

400

Simplify.

(x/6-(5x+14)/(6x))/(1/6-7/(6x)

x+2

500

Simplify.

(4-6x^-1)/(2x^-1-3x^-2)

2x

Solving Rational Expressions

100

Solve for the unknown variable x.

-5/(2x-10)-2=-5/(x-5)

S = {25/4}

200

Solve for the unknown variable.

7/(3y-9)-2=6/(y-3)

S={43/6}

300

Solve.

y/(y-3)-30/(y^2 -9)=5/(y+3)

S={5}

400

Solve.

x/(x+2)+8/(x+5)=(x-19)/(x^2+7x+10)

S={-7}

500

Solve.

-12/(v^2-3v-28)=(2v)/(v+4)

S={-1,-6}