to go from
a/c divide (-b)/c
to this
a/c - b/c
I don't know what axiom it is or how I go from that to that
To simplify the expression (a/c) / (-b/c) and convert it to the expression a/c - b/c, you can follow these steps:
Step 1: Distribute the negative sign (-) to the numerator:
-b/c = (-1)(b/c) = (-b) / c
Step 2: Rewrite the original expression with the distributed numerator:
(a/c) / (-b/c) = (a/c) * ((-c)/b)
Step 3: Simplify the expression by canceling out the common factor of c in the numerator and denominator:
(a/c) * ((-c)/b) = (a * (-c)) / (c * b)
Step 4: Simplify further:
(a * (-c)) / (c * b) = (-ac) / (cb)
Step 5: Swap the positions of the numerator and denominator to get the desired expression:
(-ac) / (cb) = -ac / cb = -a/c * c/b = -a/c + c/b
Hence, (a/c) / (-b/c) simplifies to -a/c + c/b.