How do you change the fraction #(w-3)/(w+5)# into an equivalent fraction with the denominator #w^2 + w - 20#?

1 Answer
Carl S.
Apr 10, 2018

multiply it by #{w -4}/{w -4}# to get #{(w-3)(w-4)}/{w^2 + w - 20}#

Explanation:

multiply it by #{w -4}/{w -4}#

Basically you want to solve the equation #(w+5)x = w^2 + w - 20#

As you can clearly see, you will be left with a quadratic expression as the denominator. Therefore #x# should be in the form #(w-a)# where a is some integer. So that leaves us with the equation

#(w+5)(w-a) = w^2 + w - 20#

We can factorize the right hand side to #(w+5)(w-4)# and that makes it pretty clear that a is 4 as #(w+5)(w-a)=(w+5)(w-4)#.
Hence, we need to multiply the fraction by #{w -4}/{w -4}#. Of course, since #{w -4}/{w -4}=1# the value of the expression will not change.

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