Solving for variables

[CB1101]

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

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

Could someone help me with the next step? thanks

 

[HallsofIvy]

Two ways to go. Myself, seeing that x/a has a in the denominator and you want it in the numerator, I would "invert" both sides: \(\displaystyle \frac{a}{x}= \frac{1}{1- by- cz}\). Notice that the entire right side is in the denominator, not just "1/by" and "1/cz". Some people have trouble remembering that and find it easier to do it "step by step": multiply both sides of \(\displaystyle \frac{a}{x}= 1- by- cz\) by x to get \(\displaystyle a= x(1- by- cz)\), then divide both sides by \(\displaystyle x= \frac{a}{1- by- cz}\).

 

[CB1101]

Turn right side into a fraction:
x / a = (bc - cy - bz) / (bc)

Criss-cross multiplication:
a(bc - cy - bz) = bcx

Finish it.

a = (bcx)/(bc-cy-bz)

Could you explain how you turned the right side into a fraction?

 

[stapel]

Could you explain how you turned the right side into a fraction?

Convert to a common denominator. Combine.

If you get stuck in the process, please reply showing your steps, so we can help you complete the process. Thank you!