How do you simplify $\frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }$ ?

Question

1207 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-03T00:31:45

$" "$
$color(red)(\frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }=x^2/(x^3-11x^2+24x+36)$

$" "$
We have the rational expression:

$color(blue)(\frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }$

Using the identity: $color(green)((a-b)^2 -= (a^2-2ab+b^2)$

$rArr x^2/[(x^2-12x+36)*(x+1)]$

Multiply both the factors at the denominator:

$rArr [(x^2-12x+36)*(x+1)]$

$rArr x(x^2-12x+36)+1(x^2-12x+36)$

$rArr x^3-12x^2+36x+x^2-12x+36$

Combine the like terms and simplify:

$rArr x^3-12x^2+x^2+36x-12x+36$

$rArr x^3-11x^2+24x+36$

In the next step, write the numerator with the above simplified denominator:

$rArr x^2/[x^3-11x^2+24x+36]$

Hence,

$color(green)(\frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }=x^2/(x^3-11x^2+24x+36)$

Hope this helps.

How do you simplify \frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }\frac { x ^ { 2} } { ( x - 6) ^ { 2} ( x + 1) }?