Question 147445
{{{(6)/(2-x)+(6)/(x+7)=(61)/(2-x)}}} Start with the given equation.



{{{cross((2-x))(x+7)((6)/cross((2-x)))+(2-x)cross((x+7))((6)/cross((x+7)))=cross((2-x))(x+7)((61)/cross((2-x)))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{(2-x)(x+7)}}}. Doing this will eliminate all of the fractions.



{{{6(x+7)+6(2-x)=61(x+7)}}} Simplify.



{{{6x+42+12-6x=61x+427}}} Distribute.



{{{54=61x+427}}} Combine like terms on the left side.



{{{0=61x+427-54}}} Subtract {{{54}}} from both sides.



{{{-61x=427-54}}} Subtract {{{61x}}} from both sides.



{{{-61x=373}}} Combine like terms on the right side.



{{{x=(373)/(-61)}}} Divide both sides by {{{-61}}} to isolate {{{x}}}.



{{{x=-373/61}}} Reduce.



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Answer:


So the answer is {{{x=-373/61}}} 



Which approximates to {{{x=-6.115}}}