What is the answer to (2x+3)/(2x-1)=(x-5)/(x+3) ?

The answer to (2x+3)/(2x-1)=(x-5)/(x+3) is x=-1/5

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(2x+3)/(2x-1)=(x-5)/(x+3)

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

x = - \frac{1}{5}

Decimal Notation

x = - 0.2

Solution steps

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

Cross multiply

2 x^{2} + 9 x + 9 = 2 x^{2} - 11 x + 5

Move

9

to the right side

2 x^{2} + 9 x = 2 x^{2} - 11 x - 4

Subtract

2 x^{2} - 11 x

from both sides

2 x^{2} + 9 x - (2 x^{2} - 11 x) = 2 x^{2} - 11 x - 4 - (2 x^{2} - 11 x)

Simplify

20 x = - 4

Divide both sides by

20

x = - \frac{1}{5}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{2}, x = - 3

Combine undefined points with solutions:

x = - \frac{1}{5}

\frac{60}{t - 5} - \frac{18}{t} = \frac{40}{t}

- \frac{3}{5} = \frac{3}{3 - j}

\frac{1}{x ^{4}} = 0

\frac{2 x ^{2} - x}{3} - 4 = \frac{3}{x}

x, y = x^{- 2}

What is the answer to (2x+3)/(2x-1)=(x-5)/(x+3) ?
The answer to (2x+3)/(2x-1)=(x-5)/(x+3) is x=-1/5
Solve for x: (2x+3)/(2x-1)=(x-5)/(x+3)
The solution is x=-1/5