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

The answer to (sqrt(x^2-x-1))/(x-1)=1 is x=2

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(sqrt(x^2-x-1))/(x-1)=1

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

x = 2

Solution steps

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

Multiply both sides by

x - 1

\frac{x ^{2} - x - 1}{x - 1} (x - 1) = 1 \cdot (x - 1)

Simplify

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

Square both sides:

x^{2} - x - 1 = x^{2} - 2 x + 1

x^{2} - x - 1 = x^{2} - 2 x + 1

Solve

x^{2} - x - 1 = x^{2} - 2 x + 1 : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

x^{2} + 1 = x + 1

x = 2 x 16 - x^{2}

x + 6 = 3 x^{2} - 5 x - 5

4 x - 1 = 7

4 x - 1 = 9

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