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 2 years ago
I need to simplify the ratio: x^2x20 / 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?
 2 years ago
I need to simplify the ratio: x^2x20 / 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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gezimbasha
 2 years ago
Best ResponseYou've already chosen the best response.0Solve for the roots of the first equation, by using the quadratic formula\[x=\frac{b \pm \sqrt{b^24ac}}{2a}=\frac{1 \pm \sqrt{14*1*(20)}}{2}=\frac{1 \pm \sqrt{1+80}}{2}\]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\[x^2x20 = (xx1)(xx2)\]So just replace the x1 and x2.\[(x5)(x+4)\]

TlJesusFreak37
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, 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.

gezimbasha
 2 years ago
Best ResponseYou've already chosen the best response.0No no, you get this\[\frac{(x5)(x+4)}{(x+4)(x+4)}=\frac{x5}{x+4}\]

TlJesusFreak37
 2 years ago
Best ResponseYou've already chosen the best response.0How? The middle term on the top doesn't have a coefficient. If it did, then that's what you would do since you would be finding the product of the last term that also made a sum equal to the middle term. There is no middle term though, it's just x.

gezimbasha
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, the middle term has a coefficient. It is 1. Because 1*x=x. That is why I replaced 1 in the quadratic formula.

TlJesusFreak37
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, I understand now. Thank you. (:

gezimbasha
 2 years ago
Best ResponseYou've already chosen the best response.0Are you sure? I can provide more explanation if you need? Don't hesitate please!
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