solve the given formula for the variable a. r=ab/a+b
if it is as you typed it then
r = (a/a) b + b
and a can be any real number
To solve the formula for the variable 'a', we need to isolate 'a' on one side of the equation. Let's start by multiplying both sides of the equation by (a + b):
r(a + b) = ab
Next, distribute r to both terms on the left side of the equation:
ra + rb = ab
Now, let's move all terms involving 'a' to one side of the equation by subtracting 'ab' from both sides:
ra - ab + rb = ab - ab
This simplifies to:
ra - ab + rb = 0
Next, factor out the common term 'a' on the left side:
a(r - b) + rb = 0
Finally, to isolate 'a', divide both sides of the equation by (r - b):
a = -rb / (r - b)
Therefore, the formula for the variable 'a' is a = -rb / (r - b).