Question 132602
{{{ 3/(x-2) + 5/(x+2) = 4x^2/(x^2-4) }}} Start with the given equation



{{{ 3/(x-2) + 5/(x+2) = 4x^2/((x-2)(x+2)) }}} Factor {{{x^2-4}}} to get {{{(x-2)(x+2)}}}



Notice how the LCD is {{{(x-2)(x+2)}}}




{{{((x-2)(x+2))((3)/(cross(x-2))+(5)/(cross(x+2)))=cross((x-2)(x+2))((4x^2)/(cross((x-2)(x+2))))}}} Multiply both sides by the LCD {{{(x-2)(x+2)}}}. Doing this will eliminate every fraction.



{{{3(x+2)+5(x-2)=4x^2}}} Distribute and multiply. Notice every denominator has been canceled out.



{{{3x+6+5x-10=4x^2}}} Distribute again



{{{8x-4=4x^2}}} Combine like terms



{{{8x-4-4x^2=0}}}  Subtract {{{4x^2}}} from both sides. 



{{{-4x^2+8x-4=0}}}  Rearrange the terms



{{{-4(x-1)(x-1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-1=0}}} or  {{{x-1=0}}} 


{{{x=1}}} or  {{{x=1}}}    Now solve for x in each case



Since we have a repeating answer, our only answer is {{{x=1}}}



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Answer:


So the solution is {{{x=1}}}