Question 198863


{{{(x)/(x-8)+(6)/(x-4)=(x^2)/(x^2-12x+32)}}} Start with the given equation.



{{{(x)/(x-8)+(6)/(x-4)=(x^2)/((x-8)(x-4))}}} Factor the last denominator.



{{{cross((x-8))(x-4)((x)/cross((x-8)))+(x-8)cross((x-4))((6)/cross((x-4)))=cross((x-8)(x-4))((x^2)/cross((x-8)(x-4)))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{(x-8)(x-4)}}}. Doing this will eliminate all of the fractions.



{{{x(x-4)+6(x-8)=x^2}}} Simplify



{{{x^2-4x+6x-48=x^2}}} Distribute



{{{x^2-4x+6x-48-x^2=0}}} Subtract {{{x^2}}} from both sides.



{{{2x-48=0}}} Combine like terms.



{{{2x=0+48}}} Add {{{48}}} to both sides.



{{{2x=48}}} Combine like terms on the right side.



{{{x=(48)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=24}}} Reduce.



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Answer:


So the solution is {{{x=24}}}