Operations of Rational Expressions

Simplifying Rational Expressions

100

(4x^2)/(2x)

2x, x ne 0

200

(x^2-64)/(3x-24)

(x+8)/3, x ne 8

300

(4x-16)/(x^2-8x+16)

4/(x-4), x ne 4

400

(x^2+2x-24)/(3x^2+12x-36)

(x+6)/(3(x-2)), x ne 2, -6

500

(5x^2+20x)/(x^2+6x+8)

(5x)/(x+2), x ne 2, 4

Multiplication

100

(2x)/(6x^2)* (3x^2y)/(y^3

x/y^2, x ne 0, y ne 0

200

(8x-4)/(10x-5)*(5x-15)/(3x-9)

4/3, x ne 1/2, 3

300

(x^2-4)/(x^2-1)*(x+1)/(x^2+2x)

(x-2)/(x(x-1)), x ne 1, -1, -2, 0

400

(x^2-5x+6)/(x^2-121)*(x^2+3x+2)/(x^2-2x-3)

((x-2)(x+2))/((x-11)(x+11)), x ne11, -11, 3, -1

500

(4x^3+2x^2)/(x^2+6x-7)*(x^2+x-42)/(4x^2+8x)

(x(2x+1)(x-6))/(2(x-1)(x+2)), x ne 1, -2, -1, 7

Division

100

3/(2x)div6/(7y)

(7y)/(4x), x ne 0, y ne 0

200

(3x-12)/(2x+4)div(6x-24)/(4x+8)

1, x ne -2, 4

300

(x^2-9)/x^2div(x^2-4x)/(x^2-x-12)

((x-3)(x+3)(x+3))/x^2, x ne 0, 4, -3

400

(x^2-5x+6)/x^3div(x^2+3x-10)/(4x^2)

(4(x-3)(x+5))/x, x ne 0, -5, 2

500

(6x+6y)/(x-y)div18/(5x-5y)

(5(x+4))/3, x ne y

Addition

100

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

(3x+2)/(x-2), x ne 2

200

(4x)/(x+1)+(3)/(x-3)

(4x^2-9x-3)/((x+1)(x-3)), x ne -1, 3

300

(-4x^2)/(3x-12)+(2x)/(4x^2-12x-16)

(-16x^3-16x^2+6x)/(12(x-4)(x+1)), x ne 4, -1

400

(-5x)/(x^2-3x-40)+(3)/(x-5)

(-2x^2+16x-120)/((x-5)(x-8)(x+5)), x ne 5, 8, -5

500

(2x)/(x^3+3x^2-28x)+(3)/(2x^2+30x+112)

(7x^2+20x)/(2x(x+7)(x-4)(x+8)), x ne 0, -7, 4, -8

Subtraction

100

(x^2-1)/(5y)-(x-5)/(5y)

(x^2-x+4)/(5y), y ne 0

200

x^2/(x+5)-2/(x^2-2x-35)

(x^3-7x^2-2x-10)/((x+5)(x-7)), x ne -5, 7 

300

6/(5x^2)-(3x)/(5x^2+15x)

(-3x^2+6x+18)/(5x^2(x+3)), x ne 0, -3

400

(2x)/(x^2-9)-(5)/(x^2+x-6)

(2x^2-9x+15)/((x-3)(x+3)(x-2)), x ne 3, -3, 2

500

7/(xy^2)-3/(x^2y)-15/(xy)

(7x-3y-15xy)/(x^2y^2), x ne 0, y ne 0