How do you combine #w+2+1/(w-2)#?

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Answer 1 · 2017-07-18T12:33:56

See a solution process below:

To combine these terms we need to have them all over a common denominator. Therefore, we need to multiply #(w + 2)# by the appropriate form of #1#:

#((w - 2)/(w - 2) xx (w + 2)) + 1/(w - 2) =>#

#(w^2 + 2w - 2w - 4)/(w - 2) + 1/(w - 2) =>#

#(w^2 + [2w - 2w] - 4)/(w - 2) + 1/(w - 2) =>#

#(w^2 + 0 - 4)/(w - 2) + 1/(w - 2) =>#

#(w^2 - 4)/(w - 2) + 1/(w - 2)#

We can now add the numerators over the common denominator:

#(w^2 - 4 + 1)/(w - 2) =>#

#(w^2 - 3)/(w - 2)#