Question 119347
Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me.
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The problem as I see it:
{{{x/((x-2))}}} - {{{((x+1))/x}}} = {{{8/((x^2-2x))}}}
Note that on the last denominator we can factor out x:
{{{x/((x-2))}}} - {{{((x+1))/x}}} = {{{8/(x(x-2))}}}
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Our common denominator will be x(x-2); Multiple equation by this
x(x-2)*{{{x/((x-2))}}} - x(x-2)*{{{((x+1))/x}}} = x(x-2)*{{{8/(x(x-2))}}}
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Cancel out the denominators and you have:
x(x) - (x-2)(x+1) = 8
:
x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)
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x^2 - x^2 + x + 2 = 8; removed the brackets, changed the signs
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x = 8 - 2
:
x = 6
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Check our solution in the original equation:
{{{x/((x-2))}}} - {{{((x+1))/x}}} = {{{8/((x^2-2x))}}}
Substitute 6 for x
{{{6/((6-2))}}} - {{{((6+1))/6}}} = {{{8/((6^2-2(6)))}}}
{{{6/(4)}}} - {{{(7)/6}}} = {{{8/((36-12))}}}
Put all fraction over 24:
{{{36/(24)}}} - {{{(28)/24}}} = {{{8/(24))}}}; confirms our solution
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Did you have any problem understanding what we did here?  Let me know