Rational expressions

Question

Hello

Let a and b be natural numbers such that a>b. Which of the following rational expressions are greater?

(a²-b²)/(a-b) or (a²+b²)/(a+b)

Answer 1

(a^2-b^2)/(a-b)>(a^2+b^2)/(a+b) because of the following....

(a^2-b^2)/(a-b)=(a-b)(a+b)/(a-b)=(a+b)

(a+b)/1=(a+b)(a+b)/(1)(a+b)=(a^2+2ab+b^2)/(a+b)

(a^2+2ab+b^2)/(a+b)>(a^2+b^2)/(a+b) because (a^2+2ab+b^2)>(a^2+b^2) by 2ab more