Question

Write as a single fraction with the denominator in factored form (please show work if you can)( (7x^2+5x)/(x^2+1) - (5x/(x^2-6))

Answer 1

First, see if you can factor x^2-6

Then \[\frac{7x^2+5x}{x^2+1} - \frac{5x}{x^2-6}\] find your GCD (greatest common denominator)


Quick reminder of how GCD works using simple numbers:
\[\frac{1}{2}+\frac{2}{3}= \frac{1*(\cancel{2}*3)}{2*(\cancel{2}*3)}+\frac{2*(2*\cancel{3})}{3*(2*\cancel{3})}=\frac{3+4}{6}=\frac{7}{6}\]

Answer 2

So the numerator your first is going to be everything EXCEPT \((x^2+1)\)
You'll multiply it by \((x^2-6)\)

And the numerator of your second is going to be everything EXCEPT \((x^2-6)\)
You'll multiply it by \((x^2+1)\)

You don't have to FOIL the denominator, as per your question's directions. It says it wants to you leave it as is. Just \((x^2+1)(x^2-6)\)


Make sense now?