Question

Simplify. x+5/x^2+6x+5

1/x+1; where x ≠ -1
1/x+1; where x ≠ -1, -5
1/x-5; where x ≠ 5
x-5

Answer 1

x+5/x^2+6x+5
x+5/(x+5)(x+1)
1/x+1

Answer 2

The correct option is 2.

Explanation:

The given rational expression is

`(x+5)/(x^2+6x+5)`

Factorize the denominator.

The middle term can be written as 5x+x.

`(x+5)/(x^2+5x+x+5)`

`(x+5)/(x(x+5)+1(x+5))`

`(x+5)/((x+5)(x+1))`

Cancel out the common factors.

`(1)/(x+1)`

The simplified form of the given expression is
`(1)/(x+1)`. The factors of the denominator are (x+5) and (x+1), it means at x=-5 and x=-1, the value of denominator is zero.

The given expression is not defined for x=-1 and x=-5.

Therefore the correct option is 2.