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

Question

Please show work and explanation.

Answer 1

James

Clear all the fractions by multiplying through by abc

abc (x/a) + abc (y/b) + abc (z/c) = abc (1)

Simplifying

bc x + ac y + ab z = abc

Take all the terms with a to the right hand side, by subtracting acy + abz from both sides

bcx = abc - acy - abz

Factor a out from the right hand side. abc - acy - abz = a (bc -cy - bz)

So bcx = a (bc - cy - bz)

Divide both sides by (bc - cy - bz) to isolate the a

bcx / (bc - cy - bz) = a

Mike

Answer 2

x / a = 1 - (y / b) - (z / c)

x / a = (bc - cy - bz) / bc LCD

a / x = bc / (bc - cy - bz) inverses of equals are equal

a = xbc / (bc - cy - bz) multiply both sides by x