What is the answer to 2/x = x/(4x-6) ?

The answer to 2/x = x/(4x-6) is x=6,x=2

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2/x = x/(4x-6)

\frac{2}{x} = \frac{x}{4 x - 6}

x = 6, x = 2

Solution steps

\frac{2}{x} = \frac{x}{4 x - 6}

Cross multiply

2 (4 x - 6) = x^{2}

Solve

2 (4 x - 6) = x^{2} : x = 6, x = 2

x = 6, x = 2

Verify Solutions

Find undefined (singularity) points:

x = 0, x = \frac{3}{2}

Combine undefined points with solutions:

x = 6, x = 2

\frac{1}{x + 6} + \frac{2}{3 - x} = 5

\frac{x ^{2} + 5 x + 6}{x + 3} = 1

\frac{6}{x} = 0

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

\frac{( y + 1 ) ^{2}}{( y - 3 ) ^{2}} = 1