I need to simplify the ratio: x^2-x-20 / x^2+8x+16. I know that the denominator is simplified into (x+4)(x+4), But I'm unsure as to how to work the numerator. Help?

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Solve for the roots of the first equation, by using the quadratic formula\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{1 \pm \sqrt{1-4*1*(-20)}}{2}=\frac{1 \pm \sqrt{1+80}}{2}\]You then get,\[x=\frac{1 \pm \sqrt{81}}{2}=\frac{1 \pm 9}{2}\]From there you have two solutions x1=-4, and x2=5. Now the equation\[x^2-x-20 = (x-x1)(x-x2)\]So just replace the x1 and x2.\[(x-5)(x+4)\]

Alright, but isn't that solving the equation? I just need to simplify. I'm thinking I can write it out into x+x+x+4*5, and then use the x+4 in the numerator to cancel out one from the denominator, which would leave us with 5x^2 / x+4, but I'm not sure if that's correct.

No no, you get this\[\frac{(x-5)(x+4)}{(x+4)(x+4)}=\frac{x-5}{x+4}\]

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