Question

Find the ratio compounded at x + y : x − y, x³ − y³ : x² − y²

Answer 1

Compounded ratio = `(x + y)/(x - y) xx (x^3 - y^3)/(x^2 - y^2)`

Factorize the expressions:

`x^3 - y^3 = (x - y)(x^2 + xy + y^2)`

`x^2 - y^2 = (x - y)(x + y)`

Substituting these into the expression:

`(x + y)/(x - y) xx [(x - y) (x^2 + xy + y^2)]/[(x - y) (x + y)]`

= `(x + y)/(x - y) xx (x^2 + xy + y^2)/(x + y)`

= `(x^2 + xy + y^2)/(x - y)`

∴ The compounded ratio is x² + xy + y² : x − y