Question

Rational function / Adding


Please draw steps and show answer

Answer 1

(6x² +20x -5)/(x² +6x +8)

Explanation:

You want the sum of (5x)/(x+2) and (x² -5)/(x²+6x+8).

Common denominator

Each term can be expressed with the same denominator. Then the numerators can be added.

`(5x)/(x+2)+(x^2-5)/(x^2+6x+8)=(5x(x+4))/((x+2)(x+4))+(x^2-5)/((x+2)(x+4))\\\\\\=(5x^2+20x+x^2-5)/((x+2)(x+4))=\boxed{(6x^2+20x-5)/(x^2+6x+8)}`

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