Question

How do you simplify `(18x)/(x^2-5x-36) + (2x)/(x+4)`?

Answer 1

`(2x^2)/(x^2-5x-36)`

Explanation:

Lets start by taking a look at the denominator of the first fraction,

`x^2-5x-36`

It turns out that we can factor this expression to get;

`(x-9)(x+4)`

This means that we have a common term, `(x+4)`, in the denominator of both fractions. To get a common denominator, we just need to multiply the second fraction by `(x-9)/(x-9)`.

`(18x)/((x-9)(x+4)) + (2x)/((x+4))*color(red)(((x-9))/((x-9)))`

Now that we have a common denominator, we can combine the two terms into one fraction;

`(18x+2x(x-9))/((x-9)(x+4))`

Foiling the denominator, we get back `x^2-5x-36` and multiplying the `2x` in the numerator through `x-9` we get;

`(cancel(18x) + 2x^2 - cancel(18x))/(x^2-5x-36)=(2x^2)/(x^2-5x-36)`