Question

simplify 1/xy / 1/x - 1/y

Answer 1

(1)/(xy)/(1)/(x)-(1)/(y)

To divide by 1, multiply by the reciprocal.
((1)/(xy)*(1)/(1))/(x)-(1)/(y)

Multiply (1)/(xy) by 1 to get (1)/(xy).
((1)/(xy))/(x)-(1)/(y)

Multiply (1)/(x) by (1)/(xy) to get (1)/(x^(2)y).
(1)/(x^(2)y)-(1)/(y)

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is x^(2)y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(1)/(x^(2)y)-(1)/(y)*(x^(2))/(x^(2))

Complete the multiplication to produce a denominator of x^(2)y in each expression.
(1)/(x^(2)y)-(x^(2))/(x^(2)y)

Combine the numerators of all expressions that have common denominators.
(1-x^(2))/(x^(2)y)

Reorder the polynomial 1-x^(2) alphabetically from left to right, starting with the highest order term.
(-x^(2)+1)/(x^(2)y)