Solve the inequality:
(x+2)/(x^2-3x)>0

The inequality is equivalent to x(x+2)(x−3)>0 , with the additional conditions that x≠0 and x≠3 .

Since x(x+2)(x−3) only changes signs when crossing −2 , 0 and 3 , from the fact that the evaluating the polynomial at 4 yields 24 , we see that the polynomial is

positive over (3,∞)

negative over (0,3)

positive over (−2,0)

negative over (−∞,−2)

Thus the solution set for your inequality is (−2,0)∪(3,∞) .

Step-by-step explanation:

hi Rakesh here is your answer :)

#shadow

Step-by-step explanation:

It was given that, the ellipse has directrices at

The directrices has equation: , where is the eccentricity of the ellipse.

eqn(1)

The foci are at: (0,1) qnd (0,-1)

Also, the foci are given by:

eqn(2)

Solving equation (1) and (2) simultaneously we get;

and

We use the relation, to get:

.

The equation of the ellipse is given by:

We substitute the values to get:

Or