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))
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: \[\frac{1}{2}+\frac{2}{3}= \frac{1*(\cancel{2}*3)}{2*(\cancel{2}*3)}+\frac{2*(2*\cancel{3})}{3*(2*\cancel{3})}=\frac{3+4}{6}=\frac{7}{6}\]
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?
Join our real-time social learning platform and learn together with your friends!