SOLUTION: i'm stumped i tried to by making the tops the same but that didn't go anywhere so i made the bottoms the same and that still didn't get me anywhere. {{{ (x+1)/2x = (x-1)/(2x-1) }}

Algebra ->  Equations -> SOLUTION: i'm stumped i tried to by making the tops the same but that didn't go anywhere so i made the bottoms the same and that still didn't get me anywhere. {{{ (x+1)/2x = (x-1)/(2x-1) }}      Log On


   

Question 189475: i'm stumped i tried to by making the tops the same but that didn't go anywhere so i made the bottoms the same and that still didn't get me anywhere.
+%28x%2B1%29%2F2x+=+%28x-1%29%2F%282x-1%29+
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%2B1%29%2F%282x%29+=+%28x-1%29%2F%282x-1%29+ Start with the given equation


+%28x%2B1%29%282x-1%29+=+2x%28x-1%29+ Cross multiply


+%28x%2B1%29%282x-1%29+=+2x%5E2-2x+ Distribute


+2x%5E2-x%2B2x-1+=+2x%5E2-2x+ FOIL


+2x%5E2-x%2B2x-1+-+2x%5E2+%2B+2x+=0+ Get everything to the left side


+3x-1+=0+ Combine like terms.


+3x=1+ Add 1 to both sides


+x=1%2F3+ Divide both sides by 3 to isolate "x"


So the solution is x=1%2F3 which in decimal form is which approximates to

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%2B1%29%2F2x+=+%28x-1%29%2F%282x-1%29+
You must multiply each side of the equation by the same
thing so that the equation is still true.
What you should multiply each side by is 2x%2A%282x+-+1%29

On the left side, the 2x's cancel, and on the right
side, the 2x+-+1's cancel
+%282x+-+1%29%2A%28x%2B1%29+=+2x%2A%28x-1%29+
2x%5E2+%2B+x+-+1+=+2x%5E2+-+2x
Subtract 2x%5E2 from both sides
x+-+1+=+-2x
3x+=+1
x+=+1%2F3 answer
-------------
check answer:
+%28x%2B1%29%2F2x+=+%28x-1%29%2F%282x-1%29+
+%281%2F3%2B1%29%2F%282%2A%281%2F3%29%29+=+%281%2F3-1%29%2F%282%2A%281%2F3%29-1%29+
+%284%2F3%29%2F%282%2F3%29+=+%28-2%2F3%29%2F%28-1%2F3%29+
Multiply both sides by 3%2F3

4%2F2+=+-2%2F-1
2+=+2
OK