Fractions and Solution by division

Question

(1-1/x^3)/(1-1/x^2)

Answer 1

(1-1/x³)÷(1-1/x²) = [(x³-1)/x³]÷[(x²-1)/x²]

 

                         = [(x³-1)/x³]·[x²/(x²-1)]

 

                         = [(x-1)(x²+x+1)/x³]·[x²/((x-1)(x+1))]

 

                         = (x²+x+1)/[x(x+1)]