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A, B, plus, B, C, equals, A, C
Solve for A
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Solve for B
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AB+BC-AC=0
Subtract AC from both sides.
AB-AC=-BC
Subtract BC from both sides. Anything subtracted from zero gives its negation.
\left(B-C\right)A=-BC
Combine all terms containing A.
\frac{\left(B-C\right)A}{B-C}=-\frac{BC}{B-C}
Divide both sides by B-C.
A=-\frac{BC}{B-C}
Dividing by B-C undoes the multiplication by B-C.
\left(A+C\right)B=AC
Combine all terms containing B.
\frac{\left(A+C\right)B}{A+C}=\frac{AC}{A+C}
Divide both sides by A+C.
B=\frac{AC}{A+C}
Dividing by A+C undoes the multiplication by A+C.