Question 314901
For future reference, don't be shy about using parentheses especially with complicated fraction expressions. 
I think you mean like this,
1/(x+7)  +  5/(x+6)  = -1/(x^2+13x+42)
{{{1/(x+7)  +  5/(x+6)  = -1/(x^2+13x+42)}}}
{{{1/(x+7)  +  5/(x+6)  = -1/((x+7)(x+6))}}}
{{{1(x+6)+5(x+7)=-1}}}
{{{x+6+5x+35=-1}}}
{{{6x+41=-1}}}
{{{6x=-42}}}
{{{x=-7}}}
However, one of the implicit assumptions we made was that x did not equal -6 and -7 which would cause a division by zero. 
So there is no solution. 
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{{{9/(y+2)-3/(y-2)=12/(y^2-4)}}}
{{{9/(y+2)-3/(y-2)=12/((y+2)(y-2))}}}
{{{9(y-2)-3(y+2)=12}}}
{{{9y-18-3y-6=12}}}
{{{6y-24=12}}}
{{{6y=36}}}
{{{highlight(y=6)}}}