Question 147758
{{{(3)/(x^2+4x-21)+(-5)/(x^2-8x+15)=(8)/(x^2+2x-35)}}} Start with the given equation.



{{{(3)/((x+7)(x-3))+(-5)/((x-3)(x-5))=(8)/((x+7)(x-5))}}} Factor the denominators.



{{{cross((x+7))cross((x-3))(x-5)((3)/cross((x+7)(x-3)))+(x+7)cross((x-3))cross((x-5))((-5)/cross((x-3)(x-5)))=cross((x+7))(x-3)cross((x-5))((8)/cross((x+7)(x-5)))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{(x+7)(x-3)(x-5)}}}. Doing this will eliminate all of the fractions.



{{{3(x-5)-5(x+7)=8(x-3)}}} Simplify.



{{{-2x-50=8x-24}}} Combine like terms on the left side.



{{{-2x=8x-24+50}}} Add {{{50}}} to both sides.



{{{-2x-8x=-24+50}}} Subtract {{{8x}}} from both sides.



{{{-10x=-24+50}}} Combine like terms on the left side.



{{{-10x=26}}} Combine like terms on the right side.



{{{x=(26)/(-10)}}} Divide both sides by {{{-10}}} to isolate {{{x}}}.



{{{x=-13/5}}} Reduce.



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Answer:


So the answer is {{{x=-13/5}}} 



Which approximates to {{{x=-2.6}}}