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

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

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

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

x = 3

Solution steps

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

Multiply by LCM

x^{2} - 4 x + 5 = x^{2} - 3 x + 2

Move

5

to the right side

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

Subtract

x^{2} - 3 x

from both sides

x^{2} - 4 x - (x^{2} - 3 x) = x^{2} - 3 x - 3 - (x^{2} - 3 x)

Simplify

- x = - 3

Divide both sides by

- 1

x = 3

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 2

Combine undefined points with solutions:

x = 3

\frac{4}{x ^{2}} = 1

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

135 = 5 x^{- 3}

x + \frac{6}{x} = 7

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

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