What is the answer to sqrt(2x+3)-sqrt(x-2)=sqrt(x+1) ?

The answer to sqrt(2x+3)-sqrt(x-2)=sqrt(x+1) is x=3

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sqrt(2x+3)-sqrt(x-2)=sqrt(x+1)

2 x + 3 - x - 2 = x + 1

x = 3

Solution steps

2 x + 3 - x - 2 = x + 1

Remove square roots

8 x^{2} - 4 x - 24 = 4 x^{2}

Solve

8 x^{2} - 4 x - 24 = 4 x^{2} : x = 3, x = - 2

x = 3, x = - 2

Verify Solutions:

x = 3

True

, x = - 2

False

The solution is

x = 3

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

2 x = x + 5 - 1

4 x - 9 = 2 x - 4

What is the answer to sqrt(2x+3)-sqrt(x-2)=sqrt(x+1) ?
The answer to sqrt(2x+3)-sqrt(x-2)=sqrt(x+1) is x=3
Solve for x: sqrt(2x+3)-sqrt(x-2)=sqrt(x+1)
The solution is x=3