Question

Solve the inequalities (x^2-x-6)/(x^2+4x-5)>=0.

Answer 1

x>=3
-2=<x<1
x<-5

Answer 2

Now What you should do here is obtain factors of both numerator and denominator

Answer 3

\[\frac{x^2 -x -6 }{x^2 + 4x -5} \ge 0\]

Answer 4

\[\frac{(x -2)(x +3)}{(x + 5)(x - 1)} \ge 0\]

Answer 5

then plot them on number line ... and determine the sign of the whole function now this the case of > 0 ... so you should only include those intervals which give positive value of functions

Answer 6

hmm how do i see whether it has to include infinity or not?

Answer 7

sorry typo its (x + 2)(x - 3) in numerator

Answer 8

Choice given is in the attachment.

Answer 9

\[\frac{x^2-x-6}{x^2+4x-5}=\frac{(x-3)(x+2)}{(x+5)(x-1)} \ge 0\]
so the areas we test around will be -5,-2,1, and 3

----|-----|----|------|-----
-5 -2 1 3

ands its =0 when x=3 and x=-2 (so let's include that in our solution)

let \[f(x)=\frac{(x-3)(x+2)}{(x+5)(x-1)}\]

choose a number before -5 like -6 plug into f(x)
f(-6)=(-)(-)/(-)(-)=+

so (-inf,-5) is a part of out solution

now lets choose a number between -5 and -2

like -4

f(-4)=(-)(-)/(+)(-)=-

so (-5,-2) is not a part of our solution


now choose number between -2 and 1 like 0
f(0)=(-)(+)/(+)(-)=+

sp (-2,1) is a part of our solution


now choose a number between 1 and 3 like 2

f(2)=(-)(+)/(+)(+)=-

so (1,3) is not a part of our solution

now last interval to check (3,inf)

choose a number in that interval like 4

f(4)=(+)(+)/(+)(+)
so (3,inf) is a part of our solution

Answer 10

so the answer is (-inf,-5) U [-2,1) U [3,inf)

do you remember why i include -2 and 3?
because it saids =0 also

Answer 11

thanks a lot!!