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

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

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

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

x = - 1

Solution steps

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

Multiply by LCM

x (x + 3) = 3 x (x + 2) + x + 2

Solve

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

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = - 1

5 - \frac{100}{x ^{2}} = 0

\frac{x - 4}{x} = \frac{2 x + 10}{x + 4}

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

\frac{x - 3}{x - 4} + 4 = \frac{3 x}{x}

a, \frac{1}{a} = \frac{1}{b} + \frac{1}{c}

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