Question

Please help

For the rational equation, x^2+5x+6/x+3=0, what is a valid value of x?
a. -2
b.-1
c.2
d.3

Answer 1

-1

Explanation

Step 1: Multiply both sides by x+3.

x^2+5x+6=x+3

x^2+5x+6-(x-3)=x+3-(x+3)

(subtract x+3 from both sides)

x^2+4x+3=0

(x+1)(x+3)=0 (factor left side of equation)

x+1=0 or x+3=0 (Set factors equal to 0)

X=-1 or x=-3

Check answers. (Plug them in to make sure they work.)

x=-1 (Works in original equation)

x=-3 (Doesn't work in original equation)

Therefore the answer is -1

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Answer 2

The answer for the question shown above is the Option a:

a. -2

The explanation is shown below:

1- You have the following rational equation given in the problem:

(x^2+5x+6/)(x+3)=0

2- When you factor the numerator, you obtain:

(x+3)(x+2)/(x+3)=0

3- Simplifying the equation, you have:

x+2=0
x=-2