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

The answer to (2x+3)/(x-1)=sqrt(x) is x\approx 7.60258…

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

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

x \approx 7.60258 \dots

Solution steps

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

Multiply both sides by

x - 1

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

Simplify

2 x + 3 = x (x - 1)

Expand

x (x - 1) : x x - x

2 x + 3 = x x - x

Factor

x x - x : x (x - 1)

2 x + 3 = x (x - 1)

Square both sides:

4 x^{2} + 12 x + 9 = x^{3} - 2 x^{2} + x

4 x^{2} + 12 x + 9 = x^{3} - 2 x^{2} + x

Solve

4 x^{2} + 12 x + 9 = x^{3} - 2 x^{2} + x : x \approx 7.60258 \dots

x \approx 7.60258 \dots

Verify Solutions:

x \approx 7.60258 \dots

True

The solution is

x \approx 7.60258 \dots

2 x = 4

x + 1 = x + 13

x - 6 = 36 - 2 x

y, x = 25 - y^{2}

20 + 0.6 x = 60 + 0.4 x - 0.006 x^{1.6}

What is the answer to (2x+3)/(x-1)=sqrt(x) ?
The answer to (2x+3)/(x-1)=sqrt(x) is x\approx 7.60258…
Solve for x: (2x+3)/(x-1)=sqrt(x)
The solution is x\approx 7.60258…