Question 82586
Add the following rational expressions and make sure you answer is simplified:
{{{(x^3-x^2-10x)/(x^2-8x+16)}}} + {{{(-3x^2-6x+64)/(x^2-8x+16)}}} =
:
They have the same denominators so write it:
{{{((x^3-x^2-10x) + (-3x^2-6x+64))/(x^2-8x+16)}}}
:
{{{(x^3-x^2-10x - 3x^2-6x+64)/((x-4)(x-4))}}}: remove brackets, factor denominator as you did
:
{{{(x^3 - x^2 - 3x^2 - 10x - 6x + 64)/((x-4)(x-4))}}}; group like terms
:
{{{(x^3-4x^2-16x+64)/((x-4)(x-4))}}}; combined like terms
:
{{{(x^2(x-4)-16(x-4))/((x-4)(x-4))}}}; group and factor
:
{{{((x-4)(x^2-16))/((x-4)(x-4))}}}; factor out (x-4)
:
{{{((x-4)(x-4)(x+4))/((x-4)(x-4))}}}: (x^2-16) can be factored (difference of squares)
:
Cancel out both (x-4)'s and you have:
x + 4