What is the answer to (2x+1)/(sqrt(x-1))+x-3=6 ?

The answer to (2x+1)/(sqrt(x-1))+x-3=6 is x\approx 1.18630…,x\approx 3.84731…

Solve for x: (2x+1)/(sqrt(x-1))+x-3=6

The solution is x\approx 1.18630…,x\approx 3.84731…

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\frac{2 x + 1}{x - 1} + x - 3 = 6

x \approx 1.18630 \dots, x \approx 3.84731 \dots

Solution steps

\frac{2 x + 1}{x - 1} + x - 3 = 6

Multiply both sides by

x - 1

\frac{2 x + 1}{x - 1} x - 1 + x x - 1 - 3 x - 1 = 6 x - 1

Simplify

2 x + 1 + x - 1 x - 3 x - 1 = 6 x - 1

Move

2 x

to the right side

1 + x - 1 x - 3 x - 1 = 6 x - 1 - 2 x

Move

1

to the right side

x - 1 x - 3 x - 1 = 6 x - 1 - 2 x - 1

Move

6 x - 1

to the left side

x x - 1 - 9 x - 1 = - 2 x - 1

Factor

x x - 1 - 9 x - 1 : x - 1 (x - 9)

x - 1 (x - 9) = - 2 x - 1

Square both sides:

x^{3} - 19 x^{2} + 99 x - 81 = 4 x^{2} + 4 x + 1

x^{3} - 19 x^{2} + 99 x - 81 = 4 x^{2} + 4 x + 1

Solve

x^{3} - 19 x^{2} + 99 x - 81 = 4 x^{2} + 4 x + 1 : x \approx 1.18630 \dots, x \approx 3.84731 \dots, x \approx 17.96638 \dots

x \approx 1.18630 \dots, x \approx 3.84731 \dots, x \approx 17.96638 \dots

Verify Solutions:

x \approx 1.18630 \dots

True

, x \approx 3.84731 \dots

True

, x \approx 17.96638 \dots

False

The solutions are

x \approx 1.18630 \dots, x \approx 3.84731 \dots

1 = 2 π \frac{0.1628}{k}

x^{\frac{2}{3}} - \frac{4}{25} = 0

2 x - 2 x - 1 = 1

5 x + 79 = 3 x + 17

25.7 = (18.7)^{2} + x^{2}

What is the answer to (2x+1)/(sqrt(x-1))+x-3=6 ?
The answer to (2x+1)/(sqrt(x-1))+x-3=6 is x\approx 1.18630…,x\approx 3.84731…
Solve for x: (2x+1)/(sqrt(x-1))+x-3=6
The solution is x\approx 1.18630…,x\approx 3.84731…