Question 94312
{{{3/(x+2) + 2/(x-2) = 8/(x+2)(x-2)}}} Start with the given equation



{{{(x+2)(x-2)(3/(x+2) + 2/(x-2)) = (x+2)(x-2)(8/(x+2)(x-2))}}} Multiply both sides by the LCD {{{(x+2)(x-2)}}}


{{{3(x-2) + 2(x+2) = 8}}} Distribute and multiply


{{{3x-6 + 2x+4 = 8}}} Distribute again




{{{3x+2x+4=8+6}}}Add 6 to both sides



{{{3x+2x=8+6-4}}}Subtract 4 from both sides



{{{5x=8+6-4}}} Combine like terms on the left side



{{{5x=10}}} Combine like terms on the right side



{{{x=(10)/(5)}}} Divide both sides by 5 to isolate x




{{{x=2}}} Reduce

      
--------------------------------------------------------------

Answer:

So our possible answer is {{{x=2}}}



However, we must check this answer



{{{3/(x+2) + 2/(x-2) = 8/(x+2)(x-2)}}} Start with the given equation


{{{3/(2+2) + 2/(2-2) = 8/(2+2)(2-2)}}} Plug in x=2


{{{3/4 + 2/0 = 8/0}}} Simplify the denominators



Since x=2 makes two fractions have a denominator of zero, the possible solution x=2 is not valid. So there are no solutions.