multiplying fractions

Question

(X³ -1) divided by(x-1)=

Answer 1

When it comes to the difference of two cubes, the factor formula is

x³ - a³ =(x - a)(x² - xa + a²)

 

So x³ - 1 becomes:

(x - 1)(x² - x*1 + 1²)

Or simplified:

(x - 1)(x² - x + 1²)

 

The numerator and denominator both have a x-1 in it, so those cancel out to give us:

x² - x + 1²