SOLUTION: I am running out of time and I keep getting lost in this problem. Can anyone please help? Let f(x)= 8/x + 6/x+7. Find x such that f(x)-1.

Algebra ->  Rational-functions -> SOLUTION: I am running out of time and I keep getting lost in this problem. Can anyone please help? Let f(x)= 8/x + 6/x+7. Find x such that f(x)-1.      Log On


   

Question 1127648: I am running out of time and I keep getting lost in this problem. Can anyone please help?
Let f(x)= 8/x + 6/x+7. Find x such that f(x)-1.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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I am running out of time and I keep getting lost in this problem. Can anyone please help?
Let f(x)= 8/x + 6/x+7. Find x such that f(x)-1.
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You mean, for f%28x%29=1?


1=8%2Fx%2B6%2Fx%2B7
%288%2Fx%2B6%2Fx%2B7%29x=1%2Ax
8%2B6%2B7x=x
7x-x=-8-6
6x=-14
3x=-7
x=-7%2F3

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You really have this, unlike what you gave:
f(x)=8/x+6/(x+7), and f(x)=1;

8%2Fx%2B6%2F%28x%2B7%29=1
simplest denominator x%28x%2B7%29
;
x%28x%2B7%29%288%2Fx%2B6%2F%28x%2B7%29%29=x%5E2%2B7x
8%28x%2B7%29%2B6x=x%5E2%2B7x
8x%2B56%2B6x=x%5E2%2B7x
x%5E2-7x-56=0, not factorable for integers

highlight%28x=%287%2B-+sqrt%28273%29%29%2F2%29