z/m − z/n =1, if m≠n
I assume you want to solve for z.
z(1/m - 1/n) = 1
z = 1/(1/m - 1/n)
Oh, ok. let's make that a bit prettier.
1/m - 1/n = n/mn - m/mn = (n-m)/mn
so, z = mn/(n-m)
To solve the equation z/m - z/n = 1, where m is not equal to n, you can follow these steps:
Step 1: Find the common denominator by multiplying both sides of the equation by m and n. This is done to eliminate the denominators.
m * (z/m - z/n) = m * 1
n * (z/m - z/n) = n * 1
Simplifying these equations will give:
z - z(n/m) = m
z - z(m/n) = n
Step 2: Distribute z on both sides of the equations:
z - zn/m = m
z - zm/n = n
Step 3: Combine like terms on both sides of the equations:
z(1 - n/m) = m
z(1 - m/n) = n
Step 4: Simplify the expressions inside the parentheses:
z(m - n)/(m) = m
z(n - m)/(n) = n
Step 5: Multiply both sides of the equations by the respective denominator:
z(m - n) = m^2
z(n - m) = n^2
Step 6: Divide both sides of the equations by (m - n) and (n - m), respectively:
z = m^2/(m - n)
z = n^2/(n - m)
Therefore, the solutions to the equation z/m - z/n = 1, where m is not equal to n, are z = m^2/(m - n) and z = n^2/(n - m).
To solve the equation z/m - z/n = 1, where m ≠ n, we can use algebraic manipulation.
Step 1: Multiply through by the common denominator of m and n to eliminate the denominators. The common denominator is mn.
mn * (z/m) - mn * (z/n) = mn * 1
Step 2: Simplify the equation by canceling out terms.
nz - mz = mn
Step 3: Factor out z on the left side of the equation.
z(n - m) = mn
Step 4: Divide both sides of the equation by (n - m) to isolate z.
z = mn / (n - m)
This is the solution to the equation z/m - z/n = 1 when m ≠ n.