How do you evaluate (\frac { x + 1} { y + 1} ) ^ { 3} \div \frac { x ^ { 3} + 1} { y ^ { 2} - 1}(x+1y+1)3÷x3+1y21?

1 Answer
Dec 21, 2017

((x+1)/(y+1))^3-:(x^3+1)/(y^2-1)=((x+1)^2(y-1))/((y+1)^2(x^2-x+1))(x+1y+1)3÷x3+1y21=(x+1)2(y1)(y+1)2(x2x+1)

Explanation:

((x+1)/(y+1))^3-:(x^3+1)/(y^2-1)(x+1y+1)3÷x3+1y21

= ((x+1)^3)/((y+1)^3)xx(y^2-1)/(x^3+1)(x+1)3(y+1)3×y21x3+1

= ((x+1)^3)/((y+1)^3)xx((y+1)(y-1))/((x+1)(x^2-x+1))(x+1)3(y+1)3×(y+1)(y1)(x+1)(x2x+1)

= ((x+1)^2(y-1))/((y+1)^2(x^2-x+1))(x+1)2(y1)(y+1)2(x2x+1)