What is the answer to 7/x-5/4 = x/8 ?

The answer to 7/x-5/4 = x/8 is x=4,x=-14

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7/x-5/4 = x/8

\frac{7}{x} - \frac{5}{4} = \frac{x}{8}

x = 4, x = - 14

Solution steps

\frac{7}{x} - \frac{5}{4} = \frac{x}{8}

Multiply by LCM

56 - 10 x = x^{2}

Solve

56 - 10 x = x^{2} : x = 4, x = - 14

x = 4, x = - 14

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 4, x = - 14

- \frac{1}{x ^{2}} = - \frac{1}{6}

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

x^{2} - \frac{1}{x} = 0

\frac{x + 7}{3 x} = 2

y, x = \frac{z}{w - y}