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

The answer to 5/x =-4/(x-5) is x= 25/9

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

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

x = \frac{25}{9}

Solution steps

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

Cross multiply

5 x - 25 = - x \cdot 4

Move

25

to the right side

5 x = - x \cdot 4 + 25

Move

x 4

to the left side

9 x = 25

Divide both sides by

9

x = \frac{25}{9}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 5

Combine undefined points with solutions:

x = \frac{25}{9}

\frac{x}{x - 4} = 6

\frac{( a x + b )}{c x + d} = 9

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

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

- \frac{1}{x} = 0