What is the answer to x/(x+5)=(x-4)/x ?

The answer to x/(x+5)=(x-4)/x is x=20

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x/(x+5)=(x-4)/x

\frac{x}{x + 5} = \frac{x - 4}{x}

x = 20

Solution steps

\frac{x}{x + 5} = \frac{x - 4}{x}

Cross multiply

x^{2} = x^{2} + x - 20

Subtract

x^{2} + x

from both sides

x^{2} - (x^{2} + x) = x^{2} + x - 20 - (x^{2} + x)

Simplify

- x = - 20

Divide both sides by

- 1

x = 20

Verify Solutions

Find undefined (singularity) points:

x = - 5, x = 0

Combine undefined points with solutions:

x = 20

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

\frac{9}{5} = \frac{3}{x + 7}

\frac{3}{( 1 - c )} = 4

4 = \frac{2 x}{x + 1}

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