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

The answer to x/(x-2)+(x-1)/(x-3)=5 is x= 7/3 ,x=4

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

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

x = \frac{7}{3}, x = 4

Decimal Notation

x = 2.33333 \dots, x = 4

Solution steps

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

Multiply by LCM

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

Solve

x (x - 3) + (x - 1) (x - 2) = 5 (x - 2) (x - 3) : x = \frac{7}{3}, x = 4

x = \frac{7}{3}, x = 4

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3

Combine undefined points with solutions:

x = \frac{7}{3}, x = 4

\frac{6}{x + 3} = \frac{8}{x}

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

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

\frac{x - 1}{x + 1} - \frac{6}{x - 1} = 1

8 + \frac{20}{x} = \frac{4}{3}

What is the answer to x/(x-2)+(x-1)/(x-3)=5 ?
The answer to x/(x-2)+(x-1)/(x-3)=5 is x= 7/3 ,x=4
Solve for x: x/(x-2)+(x-1)/(x-3)=5
The solution is x= 7/3 ,x=4