What is the answer to 1/(x^2-2x-7)=1 ?

The answer to 1/(x^2-2x-7)=1 is x=4,x=-2

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1/(x^2-2x-7)=1

\frac{1}{x ^{2} - 2 x - 7} = 1

x = 4, x = - 2

Solution steps

\frac{1}{x ^{2} - 2 x - 7} = 1

Multiply both sides by

x^{2} - 2 x - 7

1 = x^{2} - 2 x - 7

Solve

1 = x^{2} - 2 x - 7 : x = 4, x = - 2

x = 4, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 1 + 22, x = 1 - 22

Combine undefined points with solutions:

x = 4, x = - 2

1 + \frac{x ^{2} - 5 x - 24}{3 x} = \frac{x - 6}{3 x}

\frac{4}{x - 3} + \frac{x}{2} = - 2

\frac{7}{x} = \frac{21}{9}

\frac{5}{x} + \frac{1}{3 x} = \frac{4 x}{3}

y, x = \frac{1}{y}