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

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

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

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

x = 5

Solution steps

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

Multiply by LCM

x^{2} - 6 x + 11 = x^{2} - 5 x + 6

Move

11

to the right side

x^{2} - 6 x = x^{2} - 5 x - 5

Subtract

x^{2} - 5 x

from both sides

x^{2} - 6 x - (x^{2} - 5 x) = x^{2} - 5 x - 5 - (x^{2} - 5 x)

Simplify

- x = - 5

Divide both sides by

- 1

x = 5

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 2

Combine undefined points with solutions:

x = 5

\frac{7}{x + 1} + \frac{15}{3 x - 1} = 8

\frac{6}{x} + 2 = 2

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

\frac{- 15}{x ^{2} - 5 x + 6} + \frac{1}{x - 2} = 2

\frac{7}{( x - 1 )} = 9

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