What is the answer to 2/(x-5)=(2x)/3 ?

The answer to 2/(x-5)=(2x)/3 is x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2

Solve for x: 2/(x-5)=(2x)/3

The solution is x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2

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

x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

Decimal

x = 5.54138 \dots, x = - 0.54138 \dots

Solution steps

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

Cross multiply

6 = (x - 5) \cdot 2 x

Solve

6 = (x - 5) \cdot 2 x : x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

- 9 + \frac{1}{x + 9} = - \frac{x}{x + 9}

\frac{1}{x - 1} + 7 = \frac{x}{x - 1}

x + \frac{5}{x} = - 6

\frac{1}{2 x} - \frac{4}{x} = \frac{5}{2}

\frac{6}{3 x} + \frac{5}{4} = \frac{3}{x}

What is the answer to 2/(x-5)=(2x)/3 ?
The answer to 2/(x-5)=(2x)/3 is x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2
Solve for x: 2/(x-5)=(2x)/3
The solution is x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2