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Quantitative Aptitude Question on Number Systems

If=2x2+x−6(x+2)2−(x−2)2\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}, Q=x2+3x+9(2x−3)(x2−4)\frac{x^2+3x+9}{(2x-3)(x^2-4)} and R=x2−27x4−4R=\frac{x^2-27}{x^4-4}, then find the value of PXQ÷R

A

(x+2)[2(x−3)]\frac{(x + 2)}{[2 (x - 3)]}

B

(x+2)(x−3)\frac{(x + 2)}{(x - 3)}

C

2(x+2)(x−3)\frac{(x + 2)}{(x - 3)}

D

4(x+2)(x−3)\frac{(x + 2)}{(x - 3)}

Answer

(x+2)[2(x−3)]\frac{(x + 2)}{[2 (x - 3)]}

Explanation

Solution

The correct option is (A): (x+2)2[2(x−3)]\frac{(x+2)^2}{[2(x-3)]}

P×Q÷RP \times Q÷R=2x2+x−6(x+2)2+(x−2)2×x2+3x+9(2x−3)(x2−4)×x3−27x4−16\frac{2x^2+x-6}{(x+2)^2+(x-2)^2}\times\frac{x^2+3x+9}{(2x-3)(x^2-4)}\times\frac{x^3-27}{x^4-16}

After simplifying :

x+22(x2+4×(x2+4)(x−3)\frac{x+2}{2(x^2+4}\times\frac{(x^2+4)}{(x-3)}

(x+2)2(x−3)\frac{(x+2)}{2(x-3)}.