# How do you simplify #(5(1-b)+15)/(b^2-16)#?

##### 1 Answer

#### Explanation:

There are some inteesting techniques to use to simplify this expression.

First, start by focusing on the denominator. Notice that **perfect square**

#16 = 4 * 4 = 4^2

which means that you're dealing with the *difference of two squares*

#color(blue)(a^2 - b^2 = (a-b)(a+b))#

In this case, you would have

#b^2 - 16 = b^2 - 4^2 = (b-4)(b+4)#

Now focus on the numerator. Notice that you can use *common factor* for the two terms

#5(1-b) +15 = 5 * [(1-b) + 3] = 5 * (4 - b)#

Now, you can change the sign of the terms by recognizing that

#4 - b = - (b - 4)#

The numerator will thus be equivalent to

#5(1-b) + 15 = -5 * (b-4)#

The expression will be

#(-5 * color(red)(cancel(color(black)((b-4)))))/(color(red)(cancel(color(black)((b-4))))(b+4)) = color(green)( -5/(b+4))#