SOLUTION: Solve for x: {{{a/(bx)}}} + {{{c/d}}} = e

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Question 552200: Solve for x:
a%2F%28bx%29 + c%2Fd = e

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
a%2F%28bx%29 + c%2Fd = e

a%2F%28bx%29 + c%2Fd = e%2F1

To clear of fractions, multiply through by LCD of red%28%28%28bdx%29%2F1%29%29

red%28%28%28bdx%29%2F1%29%29a%2F%28bx%29 + red%28%28%28bdx%29%2F1%29%29c%2Fd = red%28%28%28bdx%29%2F1%29%29e%2F1

red%28%28%28cross%28b%29d%2Across%28x%29%29%2F1%29%29a%2F%28cross%28b%29cross%28x%29%29 + red%28%28%28b%2Across%28d%29x%29%2F1%29%29c%2Fcross%28d%29 = red%28%28%28bdx%29%2F1%29%29e%2F1

da + bxc = bdxe

Get all terms in x on the right by subtracting bxc from both sides:

      da = bdxe - bxc

Factor bx out of the right side:

      da = bx(de - c)

Divide both sides by b(de - c)

da%2F%28b%28de-c%29%29 = %28bx%28de-c%29%29%2F%28b%28de-c%29%29

da%2F%28b%28de-c%29%29 = %28cross%28b%29x%28cross%28de-c%29%29%29%2F%28cross%28b%29%28cross%28de-c%29%29%29

da%2F%28b%28de-c%29%29 = x

x = da%2F%28b%28de-c%29%29 

Edwin