What is the answer to x/(x-2)=(x^2-4x+1)/(x-3) ?

The answer to x/(x-2)=(x^2-4x+1)/(x-3) is x\approx 0.18639…,x\approx 2.47068…,x\approx 4.34292…

Solve for x: x/(x-2)=(x^2-4x+1)/(x-3)

The solution is x\approx 0.18639…,x\approx 2.47068…,x\approx 4.34292…

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

x \approx 0.18639 \dots, x \approx 2.47068 \dots, x \approx 4.34292 \dots

Solution steps

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

Cross multiply

x (x - 3) = (x - 2) (x^{2} - 4 x + 1)

Solve

x (x - 3) = (x - 2) (x^{2} - 4 x + 1) : x \approx 0.18639 \dots, x \approx 2.47068 \dots, x \approx 4.34292 \dots

x \approx 0.18639 \dots, x \approx 2.47068 \dots, x \approx 4.34292 \dots

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3

Combine undefined points with solutions:

x \approx 0.18639 \dots, x \approx 2.47068 \dots, x \approx 4.34292 \dots

\frac{4}{Y} = \frac{18}{3 Y} + 1

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

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

\frac{4}{3 x} + \frac{5}{4} = \frac{3}{x}

x^{- 2} - 2 x^{- 1} - 15 = 0

What is the answer to x/(x-2)=(x^2-4x+1)/(x-3) ?
The answer to x/(x-2)=(x^2-4x+1)/(x-3) is x\approx 0.18639…,x\approx 2.47068…,x\approx 4.34292…
Solve for x: x/(x-2)=(x^2-4x+1)/(x-3)
The solution is x\approx 0.18639…,x\approx 2.47068…,x\approx 4.34292…