Question

What is the least common denominator of the expression below?

g2/9-g2 + 14+g/ 24g+8g2

Answer 1

\[\large \frac{g^2}{\color{green}{9-g^2}}+\frac{14+g}{\color{royalblue}{24g+8g^2}}\]Hmm so to get a common denominator, both denominators would need the same factors. If they `share` any factors right now, then we don't need to worry about those.
Let's mess with the blue term and see what happens.
If we factor an \(\large 8g\) out of each term, it gives us,\[\large \frac{g^2}{\color{green}{9-g^2}}+\frac{14+g}{\color{royalblue}{8g(3+g)}}\]

Answer 2

The green denominator is written as the `difference of squares`. We can break it down into conjugates.

\[\large \frac{g^2}{\color{green}{(3-g)(3+g)}}+\frac{14+g}{\color{royalblue}{8g(3+g)}}\]
From here, can you tell what the common denominator would be?
Bah, you ran off -_-