Solve for a x/a+y/b+z/c=1

Problem

x/a+y/b+z/c=1

Solution

1. Isolate the term containing a by subtracting the other fractions from both sides of the equation.

x/a=1−y/b−z/c

2. Find a common denominator for the terms on the right side to combine them into a single fraction.

x/a=(b*c)/(b*c)−(y*c)/(b*c)−(z*b)/(b*c)

3. Combine the terms over the common denominator b*c

x/a=(b*c−y*c−z*b)/(b*c)

4. Invert both sides of the equation to move a to the numerator.

a/x=(b*c)/(b*c−y*c−z*b)

5. Multiply both sides by x to solve for a

a=(x*b*c)/(b*c−y*c−z*b)

Final Answer

a=(b*c*x)/(b*c−c*y−b*z)

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