√((x^2+3x+2)(x^2+5x+6)/x^2(x^2+4x+3)) is equal to :

Question

\(\sqrt{\frac{(x^2+3x+2)(x^2+5x+6)}{x^2(x^2+4x+3)}}\) is equal to :

(a) x (x +1) 

(b) \(\frac{x+2}{x}\)

(c) \(\frac{x}{x+2}\)

(d) x( x + 2)

Answer 1

(b) \(\frac{x+2}{x}\)

\(\sqrt{\frac{(x^2+3x+2)(x^2+5x+6)}{x^2(x^2+4x+3)}}\)

= \(\sqrt\frac{(x+1)(x+2)(x+2)(x+3)}{x^2(x+1)(x+3)}\)

= \(\sqrt{\frac{(x+2)^2}{x^2}}\) = \(\frac{x+2}{x}\)