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

The answer to (x^2)/(x+2)=x+1 is x=-2/3

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(x^2)/(x+2)=x+1

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

x = - \frac{2}{3}

Decimal Notation

x = - 0.66666 \dots

Solution steps

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

Multiply both sides by

x + 2

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

Expand

x (x + 2) : x^{2} + 2 x

x^{2} = x^{2} + 2 x + x + 2

Add similar elements:

2 x + x = 3 x

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

Subtract

x^{2} + 3 x

from both sides

x^{2} - (x^{2} + 3 x) = x^{2} + 3 x + 2 - (x^{2} + 3 x)

Simplify

- 3 x = 2

Divide both sides by

- 3

x = - \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 2

Combine undefined points with solutions:

x = - \frac{2}{3}

u, f = \frac{uv}{u + v}

\frac{1}{2 ( 10 d - 8 )} = 3 (12)

l (x) = \frac{2 x - 5}{5 + x}

\frac{0.4}{x - 1} = \frac{10}{4.5}

\frac{x ^{2} + 3 x + 2}{x ^{2} - 1} = 4