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

You might be interested in

Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (2, 3)

lozanna [386]

Standard equation of a circle: (x-h)² + (y-k)² = r² where (h, k) is the center and r is the radius. In the case of our equation here, (x-5)² + (y+3)² = 25, we can conclude that our circle has a center at (5, -3) and a radius of 5 units.

We can use the distance formula with the center (5, -3) and our point (2, 3) to see how far away they are...if the distance between them is less than the radius of the circle, it is on the interior. If it's equal, it's on the circle. If it's greater, it's on the exterior.

Distance = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Distance = $\sqrt{(-3-3)^2+(5-2)^2}$

Distance = $\sqrt{(-6)^2+3^2}$

Distance = $\sqrt{36+9}$

Distance = $\sqrt{45}\approx6.7082$

$6.7082>5,\ so\ (2,3)\ is\ on\ the\ \boxed{exterior}$