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

The answer to x^2-2x-1= 1/(2x-3) is x\approx-0.31309…,x\approx 1.24243…,x\approx 2.57066…

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

The solution is x\approx-0.31309…,x\approx 1.24243…,x\approx 2.57066…

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

x \approx - 0.31309 \dots, x \approx 1.24243 \dots, x \approx 2.57066 \dots

Solution steps

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

Multiply both sides by

2 x - 3

x^{2} (2 x - 3) - 2 x (2 x - 3) - (2 x - 3) = 1

Solve

x^{2} (2 x - 3) - 2 x (2 x - 3) - (2 x - 3) = 1 : x \approx - 0.31309 \dots, x \approx 1.24243 \dots, x \approx 2.57066 \dots

x \approx - 0.31309 \dots, x \approx 1.24243 \dots, x \approx 2.57066 \dots

Verify Solutions

Find undefined (singularity) points:

x = \frac{3}{2}

Combine undefined points with solutions:

x \approx - 0.31309 \dots, x \approx 1.24243 \dots, x \approx 2.57066 \dots

\frac{x ^{3} - 4 x + 3}{x ^{4} + 2 x - 4} = 0

\frac{x}{3} - \frac{6}{x} = 1

\frac{1}{15} + \frac{1}{21} = \frac{1}{x}

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

\frac{8}{x} - x = 4

What is the answer to x^2-2x-1= 1/(2x-3) ?
The answer to x^2-2x-1= 1/(2x-3) is x\approx-0.31309…,x\approx 1.24243…,x\approx 2.57066…
Solve for x: x^2-2x-1= 1/(2x-3)
The solution is x\approx-0.31309…,x\approx 1.24243…,x\approx 2.57066…