Question

x2+5x+6/x+1 less than zero
$\frac{ {x}^{2} + 5x + 6}{x + 1} = 0$
use a sign chart help solve the inequality
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Answer 1

explanation-

our primary target is to make a polynomial into a fraction less form,

so I sent x+1 to 0 hence on multiplying it becomes 0

now we are left with x^2+2x+6=0

now this is where our splitting the middle term technique comes (ONLY WORKS IN TRINOMIALS)(three terms)

We take the first term coefficient which is 1 and the last term coefficient which is 6 itself, the numbers which multiply eachother to make 6 must also make the sum 5

3 x 2 = 6

3 + 2 = 5

now I placed it in the middle term making the equation x^2+2x+3x+6

We now gave two terms one group each

by taking common out of them we got (3+x) (x+2) "(1x + 2 can be taken two times if wanted but we get the same answer anyways)"

now we want this equation to be zero se we make one set 0 so the other will multiply and become 0 and there we get the answer (-3) , (-2)