Solve for a
a=2+\frac{2}{b}
b\neq 0
Solve for b
b=\frac{2}{a-2}
a\neq 2
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2ab-4=4b
Add 4b to both sides. Anything plus zero gives itself.
2ab=4b+4
Add 4 to both sides.
2ba=4b+4
The equation is in standard form.
\frac{2ba}{2b}=\frac{4b+4}{2b}
Divide both sides by 2b.
a=\frac{4b+4}{2b}
Dividing by 2b undoes the multiplication by 2b.
a=2+\frac{2}{b}
Divide 4+4b by 2b.
-4b+2ab=4
Add 4 to both sides. Anything plus zero gives itself.
\left(-4+2a\right)b=4
Combine all terms containing b.
\left(2a-4\right)b=4
The equation is in standard form.
\frac{\left(2a-4\right)b}{2a-4}=\frac{4}{2a-4}
Divide both sides by -4+2a.
b=\frac{4}{2a-4}
Dividing by -4+2a undoes the multiplication by -4+2a.
b=\frac{2}{a-2}
Divide 4 by -4+2a.
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