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

1 Answer
Oct 10, 2015

Answer:

#(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)#