Question

If \(A=\frac{x^2-y^2}{x^2-y^2}\), \(B=\frac{x+y}{x^2+y^2+xy}\) and \(C=\frac{ 3xy^2-3x^2y}{x^2-y^2}\), then find the value of AB (A+C)

• A. \(\frac{(x-y)}{(x+y)}\)
• B. \(\frac{(x-y)}{(x+y)^2}\)
• C. \(\frac{(x-y)^2}{(x+y)}\)
• D. \(\frac{(x-y)^2}{(x+y)^2}\)

Answer 1

The Correct Option is C

The correct option is (C): \(\frac{(x-y)^2}{(x+y)}\)
AB(A+C)=\(\frac{x^2-y^3}{x^2-y^2}\times\frac{x+y}{x^2+y^2+xy}(\frac{x^3-x^3}{x^3-y^2}+\frac{3xy^2-3x^2y}{x^2-y^2})\)
After simplyfying:
= \(\frac{(x-y)^3}{(x+Y)(x-y))}\)
\(=\frac{(x-y)^2}{(x+y)}\)