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

The answer to 3/(x+2)=2-6/x is x=4,x=-3/2

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3/(x+2)=2-6/x

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

x = 4, x = - \frac{3}{2}

Decimal Notation

x = 4, x = - 1.5

Solution steps

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

Multiply by LCM

3 x = 2 x (x + 2) - 6 (x + 2)

Solve

3 x = 2 x (x + 2) - 6 (x + 2) : x = 4, x = - \frac{3}{2}

x = 4, x = - \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = 4, x = - \frac{3}{2}

4 = \frac{9.2}{x}

\frac{3}{y} = \frac{2}{2 - y}

\frac{4}{5} = \frac{8}{x}

\frac{x ^{2}}{x + 180} = 90

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