Answer:
x = [tex]\frac{mn(q-p)}{n-m}[/tex]
Step-by-step explanation:
collect the fractional terms on the left side of the equation and other terms on the right side
subtract [tex]\frac{x-n}{n}[/tex] from both sides
[tex]\frac{x-m}{m}[/tex] - [tex]\frac{x-n}{n}[/tex] + p = q
subtract p from both sides
[tex]\frac{x-m}{m}[/tex] - [tex]\frac{x-n}{n}[/tex] = q - p
We require the fractions to have a common denominator of mn
multiply the numerator/denominator of the first fraction by n and the numerator/denominator of the second fraction by m
[tex]\frac{n(x-m)}{mn}[/tex] - [tex]\frac{m(x-n)}{mn}[/tex] = q - p
distribute and simplify the numerators of the fractions
[tex]\frac{nx-nm-mx+mn}{mn}[/tex] = q - p
[tex]\frac{nx-mx}{mn}[/tex] = q - p
factor out x from each term on the numerator
[tex]\frac{x(n-m)}{mn}[/tex] = q - p
multiply both sides by mn
x(n - m) = mn(q - p)
divide both sides by (n - m)
x = [tex]\frac{mn(q-p)}{n-m}[/tex] → n ≠ m
