Solve for: (a-b)/(a)-(b-a)/(b)

Expression: $\frac{ a-b }{ a }-\frac{ b-a }{ b }$

Write all numerators above the least common denominator $ab$

$\frac{ b \times \left( a-b \right)-a \times \left( b-a \right) }{ ab }$

Distribute $b$ through the parentheses

$\frac{ ab-{b}^{2}-a \times \left( b-a \right) }{ ab }$

Distribute $-a$ through the parentheses

$\frac{ ab-{b}^{2}-ab+{a}^{2} }{ ab }$

Since two opposites add up to $0$, remove them from the expression

$\frac{ -{b}^{2}+{a}^{2} }{ ab }$