Question

How do you evaluate `(\frac { x + 1} { y + 1} ) ^ { 3} \div \frac { x ^ { 3} + 1} { y ^ { 2} - 1}`?

Answer 1

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

Explanation:

`((x+1)/(y+1))^3-:(x^3+1)/(y^2-1)`

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

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

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