solve in terms of r:s=a/1-r
To solve the equation s = a/(1 - r) in terms of r, we need to isolate r on one side of the equation.
Step 1: Multiply both sides of the equation by (1 - r) to get rid of the denominator:
s(1 - r) = a
Step 2: Distribute the s to both terms on the left side of the equation:
s - sr = a
Step 3: Move the -sr term to the right side of the equation by adding sr to both sides:
s + sr = a + sr
Step 4: Factor out the common term r on the right side of the equation:
s + sr = a + r(s)
Step 5: Factor out r on the left side of the equation:
s(1 + r) = a + r(s)
Step 6: Divide both sides of the equation by (1 + r) to solve for r:
s(1 + r)/(1 + r) = (a + r(s))/(1 + r)
Simplifying:
s = (a + rs)/(1 + r)
Thus, the equation s = (a + rs)/(1 + r) can be solved for r in terms of the other variables.