What is the answer to [-x^{-2}+9(8-x)^{-2}]=0 ?

The answer to [-x^{-2}+9(8-x)^{-2}]=0 is x=2,x=-4

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[-x^{-2}+9(8-x)^{-2}]=0

[- x^{- 2} + 9 (8 - x)^{- 2}] = 0

x = 2, x = - 4

Solution steps

[- x^{- 2} + 9 (8 - x)^{- 2}] = 0

Refine

- \frac{1}{x ^{2}} + \frac{9}{( 8 - x ) ^{2}} = 0

Multiply by LCM

- (- x + 8)^{2} + 9 x^{2} = 0

Solve

- (- x + 8)^{2} + 9 x^{2} = 0 : x = 2, x = - 4

x = 2, x = - 4

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 8

Combine undefined points with solutions:

x = 2, x = - 4

\frac{2}{( 3 x - 1 )} + \frac{3}{( 2 x - 1 )} = 0

x^{- 5} = 243

\frac{( 0.2 x + 5 )}{( 3.5 x - 3 )} = \frac{2}{5}

\frac{4}{( x ^{2} + x + 3 )} + \frac{5}{( x ^{2} - 5 x + 3 )} + \frac{3}{2} x = 0

\frac{31}{5 + n} = 9

What is the answer to [-x^{-2}+9(8-x)^{-2}]=0 ?
The answer to [-x^{-2}+9(8-x)^{-2}]=0 is x=2,x=-4
Solve for x: [-x^{-2}+9(8-x)^{-2}]=0
The solution is x=2,x=-4