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natali 33 [55]
3 years ago
5

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

Mathematics
2 answers:
Alla [95]3 years ago
6 0

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.

LuckyWell [14K]3 years ago
3 0
X+5/x^2+6x+5
x+5/(x+5)(x+1)
1/x+1
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