SOLUTION: Simplify the complex fraction: 4 + 2/x / x/4 + 1/8 The first thing I have to do is multiply the first equation by the reciprocal of the second equation. After that I do not know

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Simplify the complex fraction: 4 + 2/x / x/4 + 1/8 The first thing I have to do is multiply the first equation by the reciprocal of the second equation. After that I do not know      Log On


   

Question 29480: Simplify the complex fraction:
4 + 2/x / x/4 + 1/8
The first thing I have to do is multiply the first equation by the reciprocal of the second equation. After that I do not know what to do.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%284+%2B+2%2Fx%29+%2F+%28x%2F4+%2B+1%2F8%29
hope I got it right
right away, I see 4's and 8's, so maybe I can make it simpler
multiply top and bottom of fraction by 8
%288%2F8%29%2A%28%284+%2B+2%2Fx%29+%2F+%28x%2F4+%2B+1%2F8%29%29
8%2A%284+%2B+2%2Fx%29+%2F+%282%2Ax+%2B+1%29
multiply top and bottom by x
%28x%2Fx%29%2A%288%2A%284+%2B+2%2Fx%29+%2F+%282%2Ax+%2B+1%29%29
%2832%2Ax+%2B+16%29+%2F+%282%2Ax%5E2+%2B+x%29
%2816%2A%282%2Ax+%2B+1%29%29+%2F+%28x%2A+%282%2Ax+%2B+1%29%29
16+%2F+x answer
check
%284+%2B+2%2Fx%29+%2F+%28x%2F4+%2B+1%2F8%29+=+16%2Fx
multiply both sides by x
%284%2Ax+%2B+2%29+%2F+%28x%2F4+%2B+1%2F8%29+=+16
divide both sides by 16
%284%2Ax+%2B+2%29+%2F+%284%2Ax+%2B+2%29+=+1
OK
notice that 0 can't be a solution for x division by zero is not allowed