Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$ 
Let $m$ be the largest real root of the equation $$\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4.$$ Find $m$.

do we literally add all the fractions or do we do something else 
I have no clue how to solve this 

HINT:
Write the LHS as $$\left(\frac x{x-3}-1\right)+\left(\frac x{x-5}-1\right)+\left(\frac x{x-17}-1\right)+\left(\frac x{x-19}-1\right)$$ and this gives a constant term of $-4$. Equating this with the RHS, we have$$x\left(\frac1{x-3}+\frac1{x-5}+\frac1{x-17}+\frac1{x-19}\right)=x(x-11)$$ and note that $3,5$ are 'symmetrical' around $11$; that is, $17-11=11-5$ and $19-11=11-3$.
