Factoring (x-17)/(x+2) + (13)/(6)

[Amster]

I don't understand how (x-17)/(x+2) + 13/6 becomes 19 (x-4)/6(x+2) when factoring. Can someone please explain?

 

[galactus]

It's just algebra.

\(\displaystyle \frac{x-17}{x+2}+\frac{13}{6}\)

This is finding a common denominator. Same as adding fractions.

\(\displaystyle \frac{6}{6}\cdot \frac{(x-17)}{(x+2)}+\frac{13}{6}\cdot\frac{(x+2)}{(x+2)}\)

Now, we have a common denominator:

\(\displaystyle \frac{6(x-17)+13(x+2)}{6(x+2)}\)

\(\displaystyle \frac{19x-76}{6(x+2)}\)

Factor 19 out of the top:

\(\displaystyle \frac{19(x-4)}{6(x+2)}\)