# Simplifying Rational Expressions

posted by
**mike** on
.

1.4x12 / 4x

2.d+7 / d^2-49

3.t^2-25 / t^2+t-20

4.2x^2+6x+4 / 4x^2-12x-16

5.6-y / y^2-2y-24

1. 12 [4x] cancels out. so you're left with just 12.

2. 1/d-7 factor the d^2-49 to (d+7)(d-7). cancel out the (d+7)

3. (t-5)/(t-4) factor both numerator and denominator. so then it's: (t-5)(t+5)/(t+5)(t-4) cancel out the (t+5)'s

4. (x+2)/(2x-8) factor out a 2 from the numerator and factor out a 4 from the denominator. [2(x^2+3x+2)]/[4(x^2-3x-4)] then factor the polynomial expressions. so then you should have [2(x+2)(x+1)]/[4(x-4)(x+1)]. cancel out the (x+1). reduce the coefficients 2 and 4. then re-distribute the 2 in the denominator.

5. -1/(y+4) factor out a -1 from the numerator. factor the denominator. you should have -[(y-6)/(y-6)(y+4)] cancel out the (y-6).