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

The answer to x/(x-1)= 2/(x-3) is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

Solve for x: x/(x-1)= 2/(x-3)

The solution is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

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

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Decimal Notation

x = 4.56155 \dots, x = 0.43844 \dots

Solution steps

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

Cross multiply

x (x - 3) = (x - 1) \cdot 2

Solve

x (x - 3) = (x - 1) \cdot 2 : x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 3

Combine undefined points with solutions:

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

\frac{5}{x + 1} = 1 + \frac{4}{x + 2}

x - \frac{5}{4 x} = \frac{9}{4}

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

\frac{x ^{2} - 1}{x - 1} = 0

\frac{2}{5} = \frac{7}{x}

What is the answer to x/(x-1)= 2/(x-3) ?
The answer to x/(x-1)= 2/(x-3) is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2
Solve for x: x/(x-1)= 2/(x-3)
The solution is x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2