What is the answer to sqrt(2x+3)= x/(x+5)+2 ?

The answer to sqrt(2x+3)= x/(x+5)+2 is x\approx 0.77853…

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sqrt(2x+3)= x/(x+5)+2

2 x + 3 = \frac{x}{x + 5} + 2

x \approx 0.77853 \dots

Solution steps

2 x + 3 = \frac{x}{x + 5} + 2

Multiply both sides by

x + 5

2 x + 3 (x + 5) = \frac{x}{x + 5} (x + 5) + 2 (x + 5)

Simplify

2 x + 3 (x + 5) = x + 2 (x + 5)

Expand

2 x + 3 (x + 5) : 2 x + 3 x + 5 2 x + 3

Expand

x + 2 (x + 5) : 3 x + 10

2 x + 3 x + 5 2 x + 3 = 3 x + 10

Factor

2 x + 3 x + 5 2 x + 3 : (x + 5) 2 x + 3

(x + 5) 2 x + 3 = 3 x + 10

Square both sides:

2 x^{3} + 23 x^{2} + 80 x + 75 = 9 x^{2} + 60 x + 100

2 x^{3} + 23 x^{2} + 80 x + 75 = 9 x^{2} + 60 x + 100

Solve

2 x^{3} + 23 x^{2} + 80 x + 75 = 9 x^{2} + 60 x + 100 : x \approx 0.77853 \dots

x \approx 0.77853 \dots

Verify Solutions:

x \approx 0.77853 \dots

True

The solution is

x \approx 0.77853 \dots

a (3 i) = - 3

(x - 1)^{2} = 4

x^{2} - 3 x^{\frac{3}{2}} - 4 x = 0

3 x - 3 = 9

3 x - 3 = 3

What is the answer to sqrt(2x+3)= x/(x+5)+2 ?
The answer to sqrt(2x+3)= x/(x+5)+2 is x\approx 0.77853…
Solve for x: sqrt(2x+3)= x/(x+5)+2
The solution is x\approx 0.77853…