Loading [MathJax]/jax/output/HTML-CSS/jax.js
Home / Aptitude Tests / Mathematics / Simplify \( [1 ÷ (x...
Simplify [1÷(x2+3x+2)]+[1÷(x2+5x+6)]...

Simplify [1÷(x2+3x+2)]+[1÷(x2+5x+6)]

A.

2(x+1)2

B.

2(x+1)(x+2

C.

2(x+1)(x+2

D.

2(x+1)(x+3

Correct answer is D

[1÷(x2+3x+2)]+[1÷(x2+5x+6)]

= 1÷(x2+3x+2)+[1÷(x2+5x+6)]

= [1÷((x2+x)+(2x+2))]+[1÷((x2+3x)+(2x+6))]

= [1 ÷ (x(x + 2) + 2(x +1))] + [1 ÷ (x(x + 3) +2(x + 3) )]

= [1 ÷ (x + 1)(x + 2)] + [1 ÷ ((x + 3) + (x + 2))]

=((x + 3) + (x + 1)) ÷ (x + 1)(x + 2)(x + 3)

Using the L.C.M

=((x + x + 3 + 1)) ÷ (x + 1)(x + 2)(x + 3)

=(2x+4)/(x+1)(x+2)(x+3) =2(x+2)/(x+1)(x+2)(x+3)

= 2(x+1)(x+3)