Question 66289
Solve and check for X:

:

{{{x/(x-2) - (x+1)/x = 8/(x^2-2x)}}}
:
you can factor x^2 - 2x so you have
{{{x/(x-2) - (x+1)/x}}} = {{{8/(x(x-2))}}}
:
Multiply thru by x(x-2) you have:
x(x) - (x-2)(x+1) = 8
:
FOIL (x-2)(x+1):
x^2 - (x^2 - x - 2) = 8
x^2 - x^2 + x + 2 = 8; there is a minus so change the signs inside the brackets
:
x + 2 = 8
x = 8 - 2
x = 6
:
:
Check our solution in the original equation:
{{{6/(6-2) - (6+1)/6}}} = {{{8/(6^2 - 2(6)))}}}
:
{{{6/4 - 7/6}}} = {{{8/(36-12)}}}
:
{{{6/4 - 7/6}}} = {{{8/24}}}
:
Using the common denominator
{{{36/24 - 28/24}}} = {{{8/24}}}
:
Was this "wonderful help"?