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

1 Answer
Oct 10, 2015

(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)