Solve for q
q=\frac{w}{2-w}
w\neq 2
Solve for w
w=\frac{2q}{q+1}
q\neq -1
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2q-wq=w
Use the distributive property to multiply 2-w by q.
\left(2-w\right)q=w
Combine all terms containing q.
\frac{\left(2-w\right)q}{2-w}=\frac{w}{2-w}
Divide both sides by 2-w.
q=\frac{w}{2-w}
Dividing by 2-w undoes the multiplication by 2-w.
2q-wq=w
Use the distributive property to multiply 2-w by q.
2q-wq-w=0
Subtract w from both sides.
-wq-w=-2q
Subtract 2q from both sides. Anything subtracted from zero gives its negation.
\left(-q-1\right)w=-2q
Combine all terms containing w.
\frac{\left(-q-1\right)w}{-q-1}=-\frac{2q}{-q-1}
Divide both sides by -q-1.
w=-\frac{2q}{-q-1}
Dividing by -q-1 undoes the multiplication by -q-1.
w=\frac{2q}{q+1}
Divide -2q by -q-1.
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Limits
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