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

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

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

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

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

x = 2 + 5, x = 2 - 5

Decimal Notation

x = 4.23606 \dots, x = - 0.23606 \dots

Solution steps

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

Multiply both sides by

x - 2

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

Solve

x + 3 = x (x - 2) - (x - 2) : x = 2 + 5, x = 2 - 5

x = 2 + 5, x = 2 - 5

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = 2 + 5, x = 2 - 5

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

1 + \frac{1}{x - 5} = \frac{3}{x ^{2} - 7 x + 10}

x + \frac{1}{x} = 35

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

\frac{10}{x + 8} = \frac{5}{x - 8}

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