What will be the difference of the roots of the equation $$ (x^2 - 10x - 29)^{-1} + (x^2 - 10x - 45)^{-1} = 2(x^2 - 10x - 69)^{-1} $$
I actually tried to solve it but it was too lengthy to calculate with the simple method I know. I want to solve it in less time coz someone told me that it could be solved in less time. Can someone help?
$$x^2-10x-45=y$$ then
$$\frac{1}{y+16}+\frac{1}{y}=\frac{2}{y-24}$$
$$(2y+16)(y-24)=(y+16)2y \rightarrow y=-6 $$
Can you finish?