What is the answer to (3x+1)/(6x-2)=(2x+5)/(4x-13) ?

The answer to (3x+1)/(6x-2)=(2x+5)/(4x-13) is x=-3/61

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(3x+1)/(6x-2)=(2x+5)/(4x-13)

\frac{3 x + 1}{6 x - 2} = \frac{2 x + 5}{4 x - 13}

x = - \frac{3}{61}

Decimal Notation

x = - 0.04918 \dots

Solution steps

\frac{3 x + 1}{6 x - 2} = \frac{2 x + 5}{4 x - 13}

Cross multiply

12 x^{2} - 35 x - 13 = 12 x^{2} + 26 x - 10

Move

13

to the right side

12 x^{2} - 35 x = 12 x^{2} + 26 x + 3

Subtract

12 x^{2} + 26 x

from both sides

12 x^{2} - 35 x - (12 x^{2} + 26 x) = 12 x^{2} + 26 x + 3 - (12 x^{2} + 26 x)

Simplify

- 61 x = 3

Divide both sides by

- 61

x = - \frac{3}{61}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{3}, x = \frac{13}{4}

Combine undefined points with solutions:

x = - \frac{3}{61}

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

x - \frac{2 x + 3}{x + 5} = \frac{7}{x + 5}

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

6 x + 9 = \frac{13}{5 - x}

x + \frac{3}{x + 3} = \frac{7}{x + 3}

What is the answer to (3x+1)/(6x-2)=(2x+5)/(4x-13) ?
The answer to (3x+1)/(6x-2)=(2x+5)/(4x-13) is x=-3/61
Solve for x: (3x+1)/(6x-2)=(2x+5)/(4x-13)
The solution is x=-3/61