What is the answer to (sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1 ?

The answer to (sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1 is x=4

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(sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1

\frac{x + 5 - 4}{2 x + 1 - 2} = - 1

x = 4

Solution steps

\frac{x + 5 - 4}{2 x + 1 - 2} = - 1

Multiply both sides by

2 x + 1 - 2

\frac{x + 5 - 4}{2 x + 1 - 2} (2 x + 1 - 2) = - 1 \cdot (2 x + 1 - 2)

Simplify

x + 5 - 4 = - (2 x + 1 - 2)

Expand

- (2 x + 1 - 2) : - 2 x + 1 + 2

x + 5 - 4 = - 2 x + 1 + 2

Remove square roots

x^{2} + 64 x + 1024 = 288 x + 144

Solve

x^{2} + 64 x + 1024 = 288 x + 144 : x = 220, x = 4

x = 220, x = 4

Verify Solutions:

x = 220

False

, x = 4

True

The solution is

x = 4

x - 5 = - 2 x + 18

2 - x = 8 - 7 x

4 x + 2 = 3 x + 4

x + 4 = 6 x + 12

4 x^{2} - 9 = 2 2 x + 3

What is the answer to (sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1 ?
The answer to (sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1 is x=4
Solve for x: (sqrt(x+5)-4)/(sqrt(2x+1)-2)=-1
The solution is x=4