Question 76978
{{{x/((x-2))}}}-{{{((x+1))/x}}} = {{{8/((x^2-2x))}}}
:
Factor out x from (x^2 - 2x); note that x(x-2) will be the common denominator:
:
{{{x(x-2)x/((x-2))}}}-{{{(x(x-2)(x+1))/x}}} = {{{x(x-2)8/(x(x-2))}}}; multiplied equation by x(x-2)
:
Cancel out the denominators, you 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; change the signs inside when you remove the brackets
x^2 - x^2 + x = 8 - 2; note that the x^2's will cancel out
:
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}}}
:
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