What is the answer to (x-2)/(sqrt(2x-7))=sqrt(x-4) ?

The answer to (x-2)/(sqrt(2x-7))=sqrt(x-4) is x=8

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(x-2)/(sqrt(2x-7))=sqrt(x-4)

\frac{x - 2}{2 x - 7} = x - 4

x = 8

Solution steps

\frac{x - 2}{2 x - 7} = x - 4

Multiply both sides by

2 x - 7

\frac{x - 2}{2 x - 7} 2 x - 7 = x - 4 2 x - 7

Simplify

x - 2 = x - 4 2 x - 7

Square both sides:

x^{2} - 4 x + 4 = 2 x^{2} - 15 x + 28

x^{2} - 4 x + 4 = 2 x^{2} - 15 x + 28

Solve

x^{2} - 4 x + 4 = 2 x^{2} - 15 x + 28 : x = 3, x = 8

x = 3, x = 8

Verify Solutions:

x = 3

False

, x = 8

True

The solution is

x = 8

x + 9 - x = 3

2 (x + 5)^{\frac{2}{3}} - 11 = 7

x^{2} - 9 = 3 x - 11

1 + x = x

1 - \frac{9}{x ^{\frac{2}{3}}} = 0

What is the answer to (x-2)/(sqrt(2x-7))=sqrt(x-4) ?
The answer to (x-2)/(sqrt(2x-7))=sqrt(x-4) is x=8
Solve for x: (x-2)/(sqrt(2x-7))=sqrt(x-4)
The solution is x=8