Question

How do you simplify `((j^2-16)/(j^2+10j+16))/(15/(j+8))`?

Answer 1

`=(1/15)(j-2)(j+4)`

`=1/15j^2+2/15j-8/15`

Explanation:

`frac{(frac{j^2-16}{j^2+10j+16})}{(frac{15}{j+8})}`

Rather than dividing two fractions, use the fact that dividing is the same as multiplying by the reciprocal.
`=(frac{j^2-16}{j^2+10j+16})*(frac{j+8}{15})`

`=frac{(j^2-16)(j+8)}{(j^2+10j+16)(15)}`

Now factor the terms on the numerator and denominator:
`=frac{(j-4)(j+4)(j+8)}{(j+8)(j+2)(15)}`

`=frac{(j-2)(j+2)(j+4)(j+8)}{(j+8)(j+2)(15)}`

Cancel terms that occur on both the numerator and denominator:
`=frac{(j-2)cancel((j+2))(j+4)cancel((j+8))}{cancel((j+8))cancel((j+2))(15)}`

`=frac{(j-2)(j+4)}{15}`
`=(1/15)(j-2)(j+4)`
`=(1/15)(j^2+2j-8)`