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

The answer to 2/(x+3)=(2x-3)/x is x=(-1+sqrt(73))/4 ,x=(-1-sqrt(73))/4

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

The solution is x=(-1+sqrt(73))/4 ,x=(-1-sqrt(73))/4

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

x = \frac{- 1 + 73}{4}, x = \frac{- 1 - 73}{4}

Decimal Notation

x = 1.88600 \dots, x = - 2.38600 \dots

Solution steps

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

Cross multiply

2 x = (x + 3) (2 x - 3)

Solve

2 x = (x + 3) (2 x - 3) : x = \frac{- 1 + 73}{4}, x = \frac{- 1 - 73}{4}

x = \frac{- 1 + 73}{4}, x = \frac{- 1 - 73}{4}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 0

Combine undefined points with solutions:

x = \frac{- 1 + 73}{4}, x = \frac{- 1 - 73}{4}

\frac{x ^{2} + 4 x - 1}{( x + 2 ) ^{2}} = 0

1 - x - \frac{24}{72 x + 12} = 0

- \frac{x}{x + 6} - 1 = \frac{6}{x + 6}

- 2 = \frac{1}{1 + c}

\frac{17}{8} = \frac{9}{x}

What is the answer to 2/(x+3)=(2x-3)/x ?
The answer to 2/(x+3)=(2x-3)/x is x=(-1+sqrt(73))/4 ,x=(-1-sqrt(73))/4
Solve for x: 2/(x+3)=(2x-3)/x
The solution is x=(-1+sqrt(73))/4 ,x=(-1-sqrt(73))/4