Question

$\frac{a+b}{a-b}$ and $\frac{a^3-b^3}{a^3+b^3}$ are the two rational expressions, then their product is.

• A. $\frac{a^2+ab+b^2}{a^2-ab+b^2}$
• B. $\frac{a^2-ab+b^2}{a^2+ab-b^2}$
• C. $\frac{a^2-ab-b^2}{a^2+ab+b^2}$
• D. $\frac{a^2+ab+b^2}{a^2-ab-b^2}$

Answer 1

Answer: (A)

$\frac{a^2+ab+b^2}{a^2-ab+b^2}$

we know that

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$\frac{(a+b)}{(a-b)}\times \frac{a^3-b^3}{a^3+b^3}=\frac{(a+b)}{a-b}\times \frac{(a-b)(a^2+ab+b^2)}{(a+b)(a^2-ab+b^2)}$

$\therefore \frac{(a+b)}{(a-b)}\times \frac{a^3-b^3}{a^3+b^3}=\frac{(a^2+ab+b^2)}{(a^2-ab+b^2)}$

Hence the Ans is Option $\left[A\right]$