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

The answer to (1-sqrt(x))/(1+sqrt(x))=1-x is x=0,x=1

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

Solution

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

Solution

x = 0, x = 1

Solution steps

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

Multiply both sides by

1 + x

\frac{1 - x}{1 + x} (1 + x) = 1 \cdot (1 + x) - x (1 + x)

Simplify

1 - x = 1 + x - x (1 + x)

Expand

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

1 - x = 1 + x - x - x x

Factor

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

1 - x = (1 - x) (x + 1)

Expand

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

1 - x = x + 1 - x x - x

Move

1

to the right side

- x = - x x - x + x

Subtract

- x x + x

from both sides

- x - (- x x + x) = - x x - x + x - (- x x + x)

Simplify

x x - 2 x = - x

Factor

x x - 2 x : x (x - 2)

x (x - 2) = - x

Divide both sides by

x - 2

x = - \frac{x}{x - 2}

Square both sides:

x = \frac{x ^{2}}{x ^{2} - 4 x + 4}

x = \frac{x ^{2}}{x ^{2} - 4 x + 4}

Solve

x = \frac{x ^{2}}{x ^{2} - 4 x + 4} : x = 0, x = 1, x = 4

x = 0, x = 1, x = 4

Verify Solutions:

x = 0

True

, x = 1

True

, x = 4

False

The solutions are

x = 0, x = 1

Popular Examples

4x+8=33sqrt(x)

4 x + 8 = 33 x

sqrt(x)+\sqrt[3]{x}-12=0

sqrt(x+6)-sqrt(2x-4)=0

x + 6 - 2 x - 4 = 0

sqrt(2x-1)+4=7

2 x - 1 + 4 = 7

sqrt(2x+1)=x-1

2 x + 1 = x - 1

Frequently Asked Questions (FAQ)

What is the answer to (1-sqrt(x))/(1+sqrt(x))=1-x ?
The answer to (1-sqrt(x))/(1+sqrt(x))=1-x is x=0,x=1
Solve for x: (1-sqrt(x))/(1+sqrt(x))=1-x
The solution is x=0,x=1

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

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

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

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