# How do you rewrite the expression #5/(2r+8)=?/(2(r+4)(r^2+2r-8))#?

##### 1 Answer

#### Explanation:

So, you need to find what value of

The key here is to compare the two denominators and determine what would make them equal. Two fractions that have *equal denominators* are **equal** if their numerators are equal, so this will help you determine the value of

So, the denominator of the fraction that's on the left-hand side of the equation is

#2r + 8 = 2 * (r + 4)#

The denominator of the second fraction is

#2(r+4)(r^2 + 2r - 8)#

You can factor the quadratic by rewriting it as

#r^2 + 2r - 8 = r^2 + 4r - 2r - 8#

#=r * (r-2) + 4 * (r-2)#

#= (r-2)(r+4)#

The second denominator will thus be equivalent to

#2(r+4)(r^2 + 2r - 8) = 2(r+4)(r+4)(r-2)#

Notice that in order to get the two denominators to be equal, you need to multiply the first by

#5/(2(r+4)) * ((r-2)(r+4))/((r-2)(r+4)) = color(blue)(?)/(2(r+4)(r-2)(r+4))#

Thus, the

#color(blue)(?) = 5 * (r-2)(r+4)#