What is the answer to (4x}{x+5}=\frac{4x-5)/x ?

The answer to (4x}{x+5}=\frac{4x-5)/x is x= 5/3

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(4x}{x+5}=\frac{4x-5)/x

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Cross multiply

4 x^{2} = 4 x^{2} + 15 x - 25

Subtract

4 x^{2} + 15 x

from both sides

4 x^{2} - (4 x^{2} + 15 x) = 4 x^{2} + 15 x - 25 - (4 x^{2} + 15 x)

Simplify

- 15 x = - 25

Divide both sides by

- 15

x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 5, x = 0

Combine undefined points with solutions:

x = \frac{5}{3}

6 - \frac{5}{y + 2} = - \frac{4}{y - 1}

\frac{1}{x} = 0.08

\frac{1}{x} = 0.01

y, x = \frac{y + 1}{y + 2}

\frac{1}{x} = 0.25

What is the answer to (4x}{x+5}=\frac{4x-5)/x ?
The answer to (4x}{x+5}=\frac{4x-5)/x is x= 5/3
Solve for x: (4x}{x+5}=\frac{4x-5)/x
The solution is x= 5/3