Question 212166
{{{2/(Y+3)+3/(Y-4)=5/(Y+6)}}}


Step 1.  Get Rid of Denominators.  We'll start with the left side.  Multiply 


{{{(Y+3)(Y-4)}}} to both sides of equation.


{{{(Y+3)(Y-4)(2/(Y+3)+3/(Y-4))=(5(Y+3)(Y-4))/(Y+6)}}}


{{{2(Y-4)+3(Y+3)=(5(Y+3)(Y-4))/(Y+6)}}}


Step 2.  To get rid of denominator on right side.  Multiply 

{{{(Y+6)}}} to both sides of equation.


{{{(Y+6)(2(Y-4)+3(Y+3))=(Y+6)(5(Y+3)(Y-4))/(Y+6)}}}


{{{(Y+6)2(Y-4)+(Y+6)3(Y+3)=5(Y+3)(Y-4)}}}


Step 3.  Now multiply everything and collect like terms.


{{{2(Y^2+2Y-24)+3(Y^2+9Y+18)=5(Y^2-Y-12)}}}


{{{(2Y^2+4Y-48)+(3Y^2+27Y+54)=5Y^2-5Y-60}}}


{{{5Y^2+31Y+6=5Y^2-5Y-60}}}


{{{31Y+6=5Y-60}}}


{{{25Y=-66}}}


{{{Y=-66/5}}}