Operations on Rational Expressions

LCD/LCM

100

What is the LCM of :

3x and 3(x-2)

3x(x-2)

200

What is the LCM of :

2x^2 and 4x+12

4x^2(x+3)

300

What is the LCM of :

24x^2 and 8x^2-16x

24x^2(x-2)

400

What is the LCM of :

x^2-25 and x-5

(x+5)(x-5)

500

What is the LCM of :

9x^2-16 and 3x^2-2x-8

(3x-4)(3x+4)(x-2)

Complex Fractions

100

What is a complex fraction?

A fraction in a fraction.

200

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

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

300

((x/3)-6)/(10+(4/x))

(x(x-18))/(6(5x+2))

400

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

(x(x+6))/(3(3x+1))

500

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

(2(5x-2))/x

Addition/Subtraction

100

5/(2x)+3/(2x)

4/x

200

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

2

300

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

13/(6x)

400

(x-2)/(x+3)+(10x)/(x^2-9)

(x+2)/(x-3)

500

(3x)/(4x-12)-(x-5)/((x+6)(x-3))

(3x^2+14x+20)/(4(x-3)(x+6))

Multiplication

100

(6x^3y)/(xy^2)*(3x^2y)/(8x^3)

(9x)/4

200

(48x^5y^3)/(y^4)*(x^2y)/(6x^3y^2)

(8x^4)/y^2

300

((x+3)(x+1))/((x-5)(x+2))*(2(x+2))/(x(x+1))

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

400

(x^2-3x-10)/(x^2-2x-15)*(x^2+10x+21)

(x+2)(x+7)

500

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

(x-4)/(x+2)

Division

100

(8x^2y^2z)/(xz^3)÷(10xy)/(x^4z)

(4x^4y)/(5z)

200

(4x^2+20x)/(x^3+4x^2)÷1/(x^2+8x+16)

(4(x+5)(x+4))/x

300

(x^2-3x-18)/(x^2-9x+18)÷(x^2+9x+18)

1/((x-3)(x+6))

400

(x^2+12x+32)/(6x+42)÷(x^2+4x)/(x^2-49)

((x+8)(x-7))/(6x)

500

(x^2-4)/(2x^2+4x)÷(3x-6)/(x^2-3x+2)

((x-1)(x-2))/(6x)