Question 77884
x/x-2 – x+1/x = 8/x^2 – 2x
:
Assume you mean; (a few brackets would help a lot):
{{{x/((x-2))}}} – {{{((x+1))/x}}} = {{{8/((x^2-2x))}}}
:
Factor out x:
{{{x/((x-2))}}} – {{{((x+1))/x}}} = {{{8/(x(x-2))}}}
:
The common denominator is x(x-2), multiply the equation by x(x-2)
After canceling out the denominators you will 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 = 8 - 2: x^2's eliminated, subtract 2 from both sides

:
x = 6
:
:
Check solution in 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}}}
:
{{{36/24}}} – {{{28/24}}} = {{{8/24}}}; confirms our solution of x = 6
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