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

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

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3/(1-2/z)=3z

\frac{3}{1 - \frac{2}{z}} = 3 z

z = 3

Solution steps

\frac{3}{1 - \frac{2}{z}} = 3 z

Simplify

\frac{3}{1 - \frac{2}{z}} : \frac{3 z}{z - 2}

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

Multiply both sides by

z - 2

3 z = 3 z (z - 2)

Solve

3 z = 3 z (z - 2) : z = 0, z = 3

z = 0, z = 3

Verify Solutions

Find undefined (singularity) points:

z = 2, z = 0

Since the equation is undefined for:

0

z = 3

\frac{x}{x - 7} = \frac{7}{x - 7} + 8

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

\frac{15}{x} = - 5

\frac{4}{5} = \frac{20}{x}

y, x = \frac{y + 1}{2 y + 1}