Perform the addition or subtraction.

Question

x/1−x^3 − x /1+x+x^2

x

1−x3

−

x

1+x+x2

 

Answer 1

You definitely need some parentheses!

Answer 2

Recall that A³-B³ = (A-B)(A²+AB+B²)

 

So, 1-x³ = 1³-x³ = (1-x)(1+x+x²)

 

Therefore, x/(1-x³) - x/(1+x+x²)

 

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

 

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

 

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

 

             = x²/(1-x³)