SOLUTION: I need help solving this equation can you help? 5/x-1=4/x+1/2x

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Question 173605: I need help solving this equation can you help?
5/x-1=4/x+1/2x
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 5%2F%28x-1%29=%284%2Fx%29%2B%281%2F2%29%2A%28x%29 simplifies to 5%2F%28x-1%29-4%2Fx-x%2F2=0
  • Text form: 5/(x-1)=(4/x)+(1/2)*(x) simplifies to 5/(x-1)-4/x-x/2=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2F%28x-1%29=%284%2Fx%29%2B%281%2F2%29%2A%28x%29+%29
    For tutors: simplify_cartoon( 5/(x-1)=(4/x)+(1/2)*(x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2F%28x-1%29=highlight_red%28+%284%2Fx%29+%29%2B%281%2F2%29%2A%28x%29.
Remove unneeded parentheses around terms highlight_red%28+4%2Fx+%29
It becomes 5%2F%28x-1%29=highlight_green%28+4%2Fx+%29%2B%281%2F2%29%2A%28x%29.
Look at 5%2F%28x-1%29=4%2Fx%2Bhighlight_red%28+%28highlight_red%28+1%2F2+%29%29%2A%28x%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F2+%29
It becomes 5%2F%28x-1%29=4%2Fx%2Bhighlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2A%28x%29.
Look at 5%2F%28x-1%29=4%2Fx%2Bhighlight_red%28+1%2F2%2A%28highlight_red%28+x+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+x+%29
It becomes 5%2F%28x-1%29=4%2Fx%2B1%2F2%2Ahighlight_green%28+x+%29.
Look at 5%2F%28x-1%29=4%2Fx%2Bhighlight_red%28+1+%29%2F2%2Ax.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 5%2F%28x-1%29=4%2Fx%2Bx%2F2.
Look at 5%2F%28x-1%29=highlight_red%28+4%2Fx%2Bx%2F2+%29.
Moved these terms to the left highlight_green%28+-4%2Fx+%29,highlight_green%28+-x%2F2+%29
It becomes 5%2F%28x-1%29-highlight_green%28+4%2Fx+%29-highlight_green%28+x%2F2+%29=0.
Result: 5%2F%28x-1%29-4%2Fx-x%2F2=0

Universal Simplifier and Solver


Done!

Thank you,
Jojo