What is the answer to (2x-3)/(x-1)=(8x+1)/(4x+5) ?

The answer to (2x-3)/(x-1)=(8x+1)/(4x+5) is x= 14/5

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(2x-3)/(x-1)=(8x+1)/(4x+5)

\frac{2 x - 3}{x - 1} = \frac{8 x + 1}{4 x + 5}

x = \frac{14}{5}

Decimal Notation

x = 2.8

Solution steps

\frac{2 x - 3}{x - 1} = \frac{8 x + 1}{4 x + 5}

Cross multiply

8 x^{2} - 2 x - 15 = 8 x^{2} - 7 x - 1

Move

15

to the right side

8 x^{2} - 2 x = 8 x^{2} - 7 x + 14

Subtract

8 x^{2} - 7 x

from both sides

8 x^{2} - 2 x - (8 x^{2} - 7 x) = 8 x^{2} - 7 x + 14 - (8 x^{2} - 7 x)

Simplify

5 x = 14

Divide both sides by

5

x = \frac{14}{5}

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

x = \frac{14}{5}

\frac{1}{5 x} + \frac{x + 4}{x} = \frac{6}{5}

\frac{1}{7} - \frac{1}{2} = \frac{1}{x}

\frac{4}{x ^{2}} = 0

\frac{x}{x - 2} - \frac{3 x - 8}{x ^{2} - 5 x + 6} = 0

6 - x = \frac{8}{x}

What is the answer to (2x-3)/(x-1)=(8x+1)/(4x+5) ?
The answer to (2x-3)/(x-1)=(8x+1)/(4x+5) is x= 14/5
Solve for x: (2x-3)/(x-1)=(8x+1)/(4x+5)
The solution is x= 14/5