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

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

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

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

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

x = 2, x = - 2

Decimal Notation

x = 1.41421 \dots, x = - 1.41421 \dots

Solution steps

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

Simplify

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

Multiply both sides by

x - 1

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

Solve

x^{2} - x - 1 = - (x - 1) : x = 2, x = - 2

x = 2, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = 2, x = - 2

(j) \cdot \frac{( x - 2 )}{( x + 2 )} + \frac{( x + 2 )}{( x - 2 )} = 4

x + \frac{1}{x} = 3, \frac{( 5 x )}{( 4 x ^{2} - 5 x + 4 )}

\frac{1}{v} = \frac{1}{1.5} + \frac{1}{5}

\frac{3}{4 ( 2 x + 4 )} = x + 19

t, c = \frac{s}{t} 1 + \frac{s}{t ^{2}}

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