Question

Given the formula x = 1+a/1-a, rearrange the formula to solve for a.

a) a = x(1-a)
b) a = (1-x)/(1+x)
c) a = (x-1)/(x+1)
d) a = (x+1)/(1-x)

Answer 1

To solve for a in the equation x = 1+a/1-a, you can rearrange the equation by following the steps: multiply both sides by (1-a), combine like terms, add xa to both sides, rearrange terms, factor out a common factor, rearrange terms again, and finally divide by (1+x). The rearranged equation to solve for a is a = (1-x)/(1+x).

Step-by-step explanation:

The formula x = 1+a/1-a can be rearranged to solve for a by the following steps:

1. Multiply both sides of the equation by (1-a) to get x(1-a) = 1+a
2. Expand the left side of the equation to get x-xa = 1+a
3. Combine like terms on the left side of the equation to get -xa = 1+a-x
4. Add xa to both sides of the equation to get 0 = 1+a-x+xa
5. Rearrange the terms on the right side of the equation to get 0 = a-x+xa+1
6. Combine like terms on the right side of the equation to get 0 = a+xa-x+1
7. Factor out a common factor of a on the right side of the equation to get 0 = a(1+x)-x+1
8. Rearrange the terms on the right side of the equation to get 0 = (1+x)a-x+1
9. Divide both sides of the equation by (1+x) to isolate a and get a = (1-x)/(1+x)