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

Answer:

The correct option is 2.

Step-by-step explanation:

The given rational expression is

$\frac{x+5}{x^2+6x+5}$

Factorize the denominator.

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

$\frac{x+5}{x^2+5x+x+5}$

$\frac{x+5}{x(x+5)+1(x+5)}$

$\frac{x+5}{(x+5)(x+1)}$

Cancel out the common factors.

$\frac{1}{x+1}$

The simplified form of the given expression is $\frac{1}{x+1}$. 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.