SOLUTION: how do you solve and check the rational equation of {{{ 1/2x + (x-2)/2x = (x-2)/(2x+1) }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do you solve and check the rational equation of {{{ 1/2x + (x-2)/2x = (x-2)/(2x+1) }}}       Log On


   

Question 658796: how do you solve and check the rational equation of
+1%2F2x+%2B+%28x-2%29%2F2x+=+%28x-2%29%2F%282x%2B1%29+




Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
how do you solve and check the rational equation of
+1%2F2x+%2B+%28x-2%29%2F2x+=+%28x-2%29%2F%282x%2B1%29+
%28x-1%29%2F2x+=+%28x-2%29%2F%282x%2B1%29
cross=multiply
2x%28x-2%29=%28x-1%29%282x%2B1%29
2x%5E2-4x=2x%5E2-x-1
3x=1
x=1/3
check:
plug x=1/3 into original equation:
+1%2F2x+%2B+%28x-2%29%2F2x+=+%28x-2%29%2F%282x%2B1%29+
%281%2F2%2A1%2F3%29%2B%281%2F3-2%29%2F%282%2A1%2F3%29=%281%2F3-2%29%2F%282%2A1%2F3%2B1%29
1%2F%282%2F3%29%2B%28-5%2F3%29%2F%282%2F3%29=%28-5%2F3%29%2F%285%2F3%29
3/2-5/2=-1
-2/2=-1
-1=-1