Simplify the complex fraction
m^-1+z^-1/m^-1-z^-1
Negative exponents are better thought of as fractions: 1/m + 1/z / 1/m-1/z. The only difference between the numerator and the denominator is an operation sign. Do you know what to do from here?
To simplify the given complex fraction, we can follow these steps:
Step 1: Find the LCD (Least Common Denominator) of the fractions in the numerator and denominator. In this case, the denominators are m^(-1) and z^(-1). To simplify, we can rewrite these expressions as 1/m and 1/z, respectively. The LCD in this case would be mz.
Step 2: Multiply the numerator and denominator by the LCD to eliminate the fractions.
Numerator: (mz)(m^(-1) + z^(-1))
Denominator: (mz)(m^(-1) - z^(-1))
Step 3: Simplify the expression obtained in the previous step.
Numerator: mz(m^(-1) + z^(-1))
= mz/m + mz/z
= z + m
Denominator: mz(m^(-1) - z^(-1))
= mz/m - mz/z
= z - m
Step 4: Write the simplified expression by dividing the numerator by the denominator.
Simplified expression: (z + m) / (z - m)
So, the simplified complex fraction is (z + m) / (z - m).