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

The answer to 2sqrt(x-1)+2=(3x)/(x-1) is x\approx 2.79009…

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

Solution

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

Solution

x \approx 2.79009 \dots

Solution steps

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

Multiply both sides by

x - 1

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

Simplify

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

Expand

2 x - 1 (x - 1) + 2 (x - 1) : 2 x - 1 x - 2 x - 1 + 2 x - 2

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

Factor

2 x - 1 x - 2 x - 1 + 2 x - 2 : 2 (x - 1) (x - 1 + 1)

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

Square both sides:

4 x^{3} + 8 x^{2} x - 1 - 8 x^{2} + 4 x - 16 x x - 1 + 8 x - 1 = 9 x^{2}

4 x^{3} + 8 x^{2} x - 1 - 8 x^{2} + 4 x - 16 x x - 1 + 8 x - 1 = 9 x^{2}

Move

4 x^{3}

to the right side

8 x^{2} x - 1 - 8 x^{2} + 4 x - 16 x x - 1 + 8 x - 1 = 9 x^{2} - 4 x^{3}

Move

8 x^{2}

to the right side

8 x^{2} x - 1 + 4 x - 16 x x - 1 + 8 x - 1 = - 4 x^{3} + 17 x^{2}

Move

4 x

to the right side

8 x^{2} x - 1 - 16 x x - 1 + 8 x - 1 = - 4 x^{3} + 17 x^{2} - 4 x

Factor

8 x^{2} x - 1 - 16 x x - 1 + 8 x - 1 : 8 x - 1 (x^{2} - 2 x + 1)

8 x - 1 (x^{2} - 2 x + 1) = - 4 x^{3} + 17 x^{2} - 4 x

Square both sides:

64 x^{5} - 320 x^{4} + 640 x^{3} - 640 x^{2} + 320 x - 64 = 16 x^{6} - 136 x^{5} + 321 x^{4} - 136 x^{3} + 16 x^{2}

64 x^{5} - 320 x^{4} + 640 x^{3} - 640 x^{2} + 320 x - 64 = 16 x^{6} - 136 x^{5} + 321 x^{4} - 136 x^{3} + 16 x^{2}

Solve

64 x^{5} - 320 x^{4} + 640 x^{3} - 640 x^{2} + 320 x - 64 = 16 x^{6} - 136 x^{5} + 321 x^{4} - 136 x^{3} + 16 x^{2} : x \approx 2.79009 \dots, x \approx 8.31703 \dots

x \approx 2.79009 \dots, x \approx 8.31703 \dots

Verify Solutions:

x \approx 2.79009 \dots

True

, x \approx 8.31703 \dots

False

The solution is

x \approx 2.79009 \dots

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x + x - 10 = 2 - x - x

sqrt(16-x^2)=4-x

16 - x^{2} = 4 - x

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

2 x^{2} + 3 x - 2 = 0

1/2 u=sqrt(u)

\frac{1}{2} u = u

a(x)=sqrt(-x+3)

a (x) = - x + 3

Frequently Asked Questions (FAQ)

What is the answer to 2sqrt(x-1)+2=(3x)/(x-1) ?
The answer to 2sqrt(x-1)+2=(3x)/(x-1) is x\approx 2.79009…
Solve for x: 2sqrt(x-1)+2=(3x)/(x-1)
The solution is x\approx 2.79009…

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

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

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

Solve for x: 2sqrt(x-1)+2=(3x)/(x-1)