What is the answer to (sqrt(2x-2))/(x-5)=1 ?

The answer to (sqrt(2x-2))/(x-5)=1 is x=9

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(sqrt(2x-2))/(x-5)=1

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

x = 9

Solution steps

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

Multiply both sides by

x - 5

\frac{2 x - 2}{x - 5} (x - 5) = 1 \cdot (x - 5)

Simplify

2 x - 2 = x - 5

Square both sides:

2 x - 2 = x^{2} - 10 x + 25

2 x - 2 = x^{2} - 10 x + 25

Solve

2 x - 2 = x^{2} - 10 x + 25 : x = 9, x = 3

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

False

The solution is

x = 9

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

3 x + 108 - 14 = - 5

25 + x = 0

x - 6 = 5 x - 34

What is the answer to (sqrt(2x-2))/(x-5)=1 ?
The answer to (sqrt(2x-2))/(x-5)=1 is x=9
Solve for x: (sqrt(2x-2))/(x-5)=1
The solution is x=9