1. ## Simplifying Expression, help

I need step by step help on simplifying this expression:

(2x^2 - 18) / (4x^8) divided by (6x^2 + 6x - 36) / (8x^4)

2. Hello, jenbones!

$\displaystyle \text{Simplify: }\;\dfrac{2x^2 - 18}{4x^8} \div \dfrac{6x^2 + 6x - 36}{8x^4}$

First, "invert and multiply":

. . $\displaystyle \dfrac{2x^2-18}{4x^8} \cdot \dfrac{8x^4}{6x^2+6x-36}$

The first numerator factors:

. . $\displaystyle 2x^2-18 \;=\;2(x^2-9) \;=\;2(x-3)(x+3)$

The second denominator factors:

. . $\displaystyle 6x^2 + 6x - 36 \;=\;6(x^2+x-6) \;=\;6(x-2)(x+3)$

The problem becomes: .$\displaystyle \dfrac{2(x-3)(x+3)}{4x^8} \cdot \dfrac{8x^4}{6(x-2)(x+3)}$

Can you finish up?

3. Originally Posted by jenbones
I need step by step help on simplifying this expression:

(2x^2 - 18) / (4x^8) divided by (6x^2 + 6x - 36) / (8x^4)

Hi jenbones,

$\displaystyle \dfrac{2x^2-18}{4x^8} \div \dfrac{6x^2+6x-36}{8x^4}=$

$\displaystyle \dfrac{2(x^2-9)}{4x^8} \times \dfrac{8x^4}{6(x^2+x-6)}=$

$\displaystyle \dfrac{2(x+3)(x-3)}{4x^8} \times \dfrac{8x^4}{6(x+3)(x-2)}=$

$\displaystyle \dfrac{16x^4(x+3)(x-3)}{24x^8(x+3)(x-2)}=$

$\displaystyle \dfrac{2(x-3)}{3x^4(x-2)}$

Late again!

4. Originally Posted by Soroban
Hello, jenbones!

First, "invert and multiply":

. . $\displaystyle \dfrac{2x^2-18}{4x^8} \cdot \dfrac{8x^4}{6x^2+6x-36}$

The first numerator factors:

. . $\displaystyle 2x^2-18 \;=\;2(x^2-9) \;=\;2(x-3)(x+3)$

The second denominator factors:

. . $\displaystyle 6x^2 + 6x - 36 \;=\;6(x^2+x-6) \;=\;6(x-2)(x+3)$

The problem becomes: .$\displaystyle \dfrac{2(x-3)(x+3)}{4x^8} \cdot \dfrac{8x^4}{6(x-2)(x+3)}$

Can you finish up?

Yes, I can thank you