a, times, left parenthesis, b, minus, 2, right parenthesis, equals, 3, b

Solve for a

a=\frac{3b}{b-2},b\neq 2

Solve for b

b=\frac{2a}{a-3},a\neq 3

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ab-2a=3b

Use the distributive property to multiply a by b-2.

\left(b-2\right)a=3b

Combine all terms containing a.

\frac{\left(b-2\right)a}{b-2}=\frac{3b}{b-2}

Divide both sides by b-2.

a=\frac{3b}{b-2}

Dividing by b-2 undoes the multiplication by b-2.

ab-2a=3b

Use the distributive property to multiply a by b-2.

ab-2a-3b=0

Subtract 3b from both sides.

ab-3b=2a

Add 2a to both sides. Anything plus zero gives itself.

\left(a-3\right)b=2a

Combine all terms containing b.

\frac{\left(a-3\right)b}{a-3}=\frac{2a}{a-3}

Divide both sides by a-3.

b=\frac{2a}{a-3}

Dividing by a-3 undoes the multiplication by a-3.