Question

step by step explanation pls
x((1+1/x)(1+1/x+1)(1+1/x+2)–1)

options:
a)3
b)2x
c)5x
d)1​

Answer 1

Answer:

Option(a)

Step-by-step explanation:

Equation is : x * ([x + 1/x)] * [(1 + 1/(x + 1))] * [(1 + 1/(x + 2) - 1)]

=> x * [1 + (1/x + 1) * (1/x) * (1/x(x + 1))] * [(1 + 1/(x + 2) - 1)]

=> x * [(x/x(x + 1) + (x + 1)/x(x + 1) + 1/x(x + 1))] * [(1 + 1/(x + 2) - 1)]

=> x * (x + x + 1 + 1/x(x + 1)] * [(1 + 1/(x + 2) - 1)]

=> x * [2(x + 1)/x(x + 1)] * [(1 + 1/(x + 2) - 1)]

=> x * (2/x + 1) * [(1 + 1/(x + 2) - 1)]

=> x * [(2/x) + (2/x + 2) + 1 + 1/(x + 2) - 1]

=> x * (3/x + 1 - 1)

=> 3x/x

=> 3

Hence, the result is 3.

#Hope my answer helped you!

Answer 2

Answer:

My answer was A...

Explanation->

|x|<1 means x should be between -1 and 1.

from (1)

x2-1<0 => x between -1 and 1. sufficient

from (2)

if x +ve then same as 1 and sufficient

if x -ve then |x|=-x

-x2<1 or x2 > -1 not sufficient

so and A

Please correct me if wrong