What is the answer to (sqrt(3x+10)+1)/(2-sqrt(x+3))=3 ?

The answer to (sqrt(3x+10)+1)/(2-sqrt(x+3))=3 is x=-2

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(sqrt(3x+10)+1)/(2-sqrt(x+3))=3

\frac{3 x + 10 + 1}{2 - x + 3} = 3

x = - 2

Solution steps

\frac{3 x + 10 + 1}{2 - x + 3} = 3

Multiply both sides by

2 - x + 3

\frac{3 x + 10 + 1}{2 - x + 3} (2 - x + 3) = 3 (2 - x + 3)

Simplify

3 x + 10 + 1 = 3 (2 - x + 3)

Expand

3 (2 - x + 3) : 6 - 3 x + 3

3 x + 10 + 1 = 6 - 3 x + 3

Remove square roots

36 x^{2} + 504 x + 1764 = 900 x + 2700

Solve

36 x^{2} + 504 x + 1764 = 900 x + 2700 : x = 13, x = - 2

x = 13, x = - 2

Verify Solutions:

x = 13

False

, x = - 2

True

The solution is

x = - 2

b + 8 = b - 4

y, x y = 12 y - x

8 x - 8 - 1 = x

7 + 3 x = 5 x + 4 + 5

x^{2} + 2 x + 1 = 5

What is the answer to (sqrt(3x+10)+1)/(2-sqrt(x+3))=3 ?
The answer to (sqrt(3x+10)+1)/(2-sqrt(x+3))=3 is x=-2
Solve for x: (sqrt(3x+10)+1)/(2-sqrt(x+3))=3
The solution is x=-2