Question

Simplify:

`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`

Answer 1

It is known that,

a² − b² = (a + b) (a − b)

a³ − b³ = (a − b)(a² + ab + b²)

`(1 - 2x + x^2)/(1 - x^3) xx (1 + x + x^2)/(1 + x)`

= `(1 - x - x + x^2)/((1)^3 - (x)^3) xx (1 + x + x^2)/(1 + x)`

= `(1(1 - x) - x(1 - x))/((1 - x){(1)^2 + (1) xx (x) + (x)^2}) xx ((1 + x + x^2))/(1 + x)`

= `((1 - x) (1 - x))/((1 - x) (1 + x + x^2)) xx ((1 + x + x^2))/((1 + x))`

= `(1 - x)/(1 + x)`