Solve for a
a=-2+\frac{3}{b}
b\neq 0
Solve for b
b=\frac{3}{a+2}
a\neq -2
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ab=-2b+3
Add 3 to both sides.
ba=3-2b
The equation is in standard form.
\frac{ba}{b}=\frac{3-2b}{b}
Divide both sides by b.
a=\frac{3-2b}{b}
Dividing by b undoes the multiplication by b.
a=-2+\frac{3}{b}
Divide -2b+3 by b.
ab-3+2b=0
Add 2b to both sides.
ab+2b=3
Add 3 to both sides. Anything plus zero gives itself.
\left(a+2\right)b=3
Combine all terms containing b.
\frac{\left(a+2\right)b}{a+2}=\frac{3}{a+2}
Divide both sides by a+2.
b=\frac{3}{a+2}
Dividing by a+2 undoes the multiplication by a+2.
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