What is the answer to 1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0 ?

The answer to 1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0 is x=-3,x=13

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1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0

\frac{1}{( x ^{2} - 10 x - 29 )} + \frac{1}{( x ^{2} - 10 x - 45 )} - \frac{2}{( x ^{2} - 10 x - 69 )} = 0

x = - 3, x = 13

Solution steps

\frac{1}{( x ^{2} - 10 x - 29 )} + \frac{1}{( x ^{2} - 10 x - 45 )} - \frac{2}{( x ^{2} - 10 x - 69 )} = 0

Multiply by LCM

(x^{2} - 10 x - 45) (x^{2} - 10 x - 69) + (x^{2} - 10 x - 29) (x^{2} - 10 x - 69) - 2 (x^{2} - 10 x - 29) (x^{2} - 10 x - 45) = 0

Solve

(x^{2} - 10 x - 45) (x^{2} - 10 x - 69) + (x^{2} - 10 x - 29) (x^{2} - 10 x - 69) - 2 (x^{2} - 10 x - 29) (x^{2} - 10 x - 45) = 0 : x = - 3, x = 13

x = - 3, x = 13

Verify Solutions

Find undefined (singularity) points:

x = 5 + 36, x = 5 - 36, x = 5 + 70, x = 5 - 70, x = 5 + 94, x = 5 - 94

Combine undefined points with solutions:

x = - 3, x = 13

\frac{x}{( x - 1 )} - \frac{2}{( x + 1 )} = \frac{4}{( x ^{2} - 1 )}

\frac{1}{2 w + 7} = 2 w - 2

\frac{3}{( x + 2 ) - 2} = \frac{11}{2}

\frac{( x + 1 )}{( 2 x + 3 )} = \frac{3}{8}

\frac{x + 1}{x} = \frac{10}{3}

What is the answer to 1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0 ?
The answer to 1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0 is x=-3,x=13
Solve for x: 1/((x^2-10x-29))+1/((x^2-10x-45))-2/((x^2-10x-69))=0
The solution is x=-3,x=13