What is the answer to sqrt(x+3)+6/(sqrt(x+3))=5 ?

The answer to sqrt(x+3)+6/(sqrt(x+3))=5 is x=1,x=6

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sqrt(x+3)+6/(sqrt(x+3))=5

x + 3 + \frac{6}{x + 3} = 5

x = 1, x = 6

Solution steps

x + 3 + \frac{6}{x + 3} = 5

Multiply both sides by

x + 3

x + 3 x + 3 + \frac{6}{x + 3} x + 3 = 5 x + 3

Simplify

(x + 3)^{2} + 6 = 5 x + 3

Move

5 x + 3

to the left side

(x + 3)^{2} + 6 - 5 x + 3 = 0

Factor

(x + 3)^{2} + 6 - 5 x + 3 : (x + 3 - 2) (x + 3 - 3)

(x + 3 - 2) (x + 3 - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 3 - 2 = 0 or x + 3 - 3 = 0

Solve

x + 3 - 2 = 0 : x = 1

Solve

x + 3 - 3 = 0 : x = 6

x = 1, x = 6

Verify Solutions:

x = 1

True

, x = 6

True

The solutions are

x = 1, x = 6

1 - \frac{5}{120 - x} = 0

6 w - 5 + 10 = 3

4 x - 32 - 16 = - 14

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

What is the answer to sqrt(x+3)+6/(sqrt(x+3))=5 ?
The answer to sqrt(x+3)+6/(sqrt(x+3))=5 is x=1,x=6
Solve for x: sqrt(x+3)+6/(sqrt(x+3))=5
The solution is x=1,x=6