Solve for a:
1/a - 1/b = 1/c
Bring 1/a - 1/b together using the common denominator a b:
(b - a)/(a b) = 1/c
Cross multiply:
c (b - a) = a b
Expand out terms of the left hand side:
b c - a c = a b
Subtract a b + b c from both sides:
a (-b - c) = -b c
Divide both sides by -b - c:
a = (bc) / (b + c)
+26367 (1/a) - (1/b) = (1/c)
make a the subject
\(\begin{array}{|rcll|} \hline \dfrac{1}{a}-\dfrac{1}{b} &=& \dfrac{1}{c} \quad & | \quad +\dfrac{1}{b} \\\\ \dfrac{1}{a} &=& \dfrac{1}{c} +\dfrac{1}{b} \\\\ \dfrac{1}{a} &=& \dfrac{1}{c}\cdot \dfrac{b}{b} +\dfrac{1}{b}\cdot \dfrac{c}{c} \\\\ \dfrac{1}{a} &=& \dfrac{b}{bc} +\dfrac{c}{bc} \\\\ \dfrac{1}{a} &=& \dfrac{b+c}{bc} \\\\ \dfrac{a}{1} &=& \dfrac{bc}{b+c} \\\\ \mathbf{a} & \mathbf{=} & \mathbf{\dfrac{bc}{b+c}} \\\\ \hline \end{array}\)
