Question 187087
{{{5/(y+2)  - 3/(y-2)  = 4/(y^2-4)}}} Start with the given equation.



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



{{{cross((y+2))(y-2)(5/cross((y+2)))  - (y+2)cross((y-2))(3/cross((y-2)))  = cross((y+2)(y-2))(4/cross((y+2)(y-2)))}}} Multiply EVERY term by the LCD {{{(y+2)(y-2)}}} to clear the fractions.



{{{(y-2)5-(y+2)3=4}}} Simplify



{{{5(y-2)-3(y+2)=4}}} Rearrange the terms.



{{{5y-10-3y-6=4}}} Distribute.



{{{2y-16=4}}} Combine like terms on the left side.



{{{2y=4+16}}} Add {{{16}}} to both sides.



{{{2y=20}}} Combine like terms on the right side.



{{{y=(20)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



{{{y=10}}} Reduce.



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Answer:


So the answer is {{{y=10}}}