Question 96159
Solve and check for x
(x/x-2)-(x+1/x)=(8/x^2-2x)
:
{{{x/((x-2))}}}-{{{((x+1))/x}}} = {{{8/((x^2-2x))}}}
:
Factor (x^2 - 2x):
{{{x/((x-2))}}}-{{{((x+1))/x}}} = {{{8/(x(x-2))}}}
:
Multiplying equation by x(x-2) gets rid of the denominators and we have:
x(x) - (x-2)(x+1) = 8
:
x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)
:
x^2 - x^2 + x + 2 = 8: removing the brackets changes the signs
:
x + 2 = 8; x^2's eliminated
:
x = 8 - 2

x = 6
:
:
Check solution by substituting 6 for x in the original equation:
:
{{{6/((6-2))}}}-{{{((6+1))/6}}} = {{{8/((6^2-2(6)))}}}
:
{{{6/4}}} - {{{7/6}}} =  {{{8/24}}}   =   {{{36/24}}} - {{{28/24}}} = {{{8/24}}} Confirms our solution