Simplify ( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] )
-
A.
( frac{2}{(x + 1)^2} ) -
B.
( frac{2}{(x + 1)(x + 2} ) -
C.
( frac{2}{(x + 1)(x + 2} ) -
D.
( frac{2}{(x + 1)(x + 3} )
Correct Answer: Option D
Explanation
( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] )
= ( 1 ÷ (x^2 + 3x + 2) + [1 ÷ (x^2 +5x + 6)])
= ( [1 ÷ ((x^2 + x) + (2x + 2) )] + [1 ÷ ((x^2 + 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)
= ( frac{2 }{(x + 1)(x + 3)} )
There is an explanation video available below.