Question

What is the least common denominator of the expression below?

g^2 14+g
_____ + _____
9-g^2 24g+8g^2

Answer 1

Greetings from Brasil...

from notable products:

A² - B² = (A + B)·(A - B)

bringing to our problem:

9 - G² = (3 + G)·(3 - G)

Factoring 24G + 8G²:

8G(3 + G)

So, we have:

{G²/[ (3 + G)·(3 - G)]} + {(14 + G)/[8G(3 + G)]}

So the least common denominator is: 3 + G

`\large{(G^2)/(9-G^2)+(14+G)/(24G+8G^2)=(G^2)/((3+G)\cdot (3-G))+(14+G)/(8G\cdot (3+G))}`