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

The answer to x+3= 1/(x-2)+1 is x=sqrt(5),x=-sqrt(5)

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

The solution is x=sqrt(5),x=-sqrt(5)

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

x = 5, x = - 5

Decimal Notation

x = 2.23606 \dots, x = - 2.23606 \dots

Solution steps

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

Move

3

to the right side

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

Multiply both sides by

x - 2

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

Solve

x (x - 2) = 1 - 2 (x - 2) : x = 5, x = - 5

x = 5, x = - 5

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = 5, x = - 5

\frac{x}{4 x + 2} = 5

\frac{2}{x + 5} = \frac{3}{x + 4}

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

\frac{1}{x ^{3}} = 2

\frac{1}{x ^{3}} = 0

What is the answer to x+3= 1/(x-2)+1 ?
The answer to x+3= 1/(x-2)+1 is x=sqrt(5),x=-sqrt(5)
Solve for x: x+3= 1/(x-2)+1
The solution is x=sqrt(5),x=-sqrt(5)