1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Damm [24]
3 years ago
15

Solve rational inequality x²+x-6/x²-3x-4≤0?​

Mathematics
2 answers:
Fittoniya [83]3 years ago
8 0

Answer:

Step-by-step explanation:

x

2

+

x

−

6

=

(

x

+

3

)

(

x

−

2

)

x

2

−

3

x

−

4

=

(

x

−

4

)

(

x

+

1

)

Each of the linear factors occurs precisely once, so the sign of the given rational expression will change at each of the points where one of the linear factors is zero. That is at:

x

=

−

3

,

−

1

,

2

,

4

Note that when

x

is large, the

x

2

terms will dominate the values of the numerator and denominator, making both positive.

Hence the sign of the value of the rational expression in each of the intervals

(

−

∞

,

−

3

)

,

(

−

3

,

−

1

)

,

(

−

1

,

2

)

,

(

2

,

4

)

and

(

4

,

∞

)

follows the pattern

+

−

+

−

+

. Hence the intervals

(

−

3

,

−

1

)

and

(

2

,

4

)

are both part of the solution set.

When

x

=

−

1

or

x

=

4

, the denominator is zero so the rational expression is undefined. Since the numerator is non-zero at those values, the function will have vertical asymptotes at those points (and not satisfy the inequality).

When

x

=

−

3

or

x

=

2

, the numerator is zero and the denominator is non-zero. So the function will be zero and satisfy the inequality at those points.

Hence the solution is:

x

∈

[

−

3

,

−

1

)

∪

[

2

,

4

)

graph{(x^2+x-6)/(x^2-3x-4) [-10, 10, -5, 5]}

Aleonysh [2.5K]3 years ago
7 0

Answer:

x ∈ [-3;-1) ∪ [2;4)

Step-by-step explanation:

\frac{x^{2}+x-6 }{x^{2}-3x-4 }\leq 0\\=> \frac{(x-2)(x+3)}{(x+1)(x-4)} \leq 0\\

we have this board:

x                          -3                    -1                      2                     4          

x - 2          -                        -                    -           0        +                     +

x+3            -         0           +                   +                      +                     +

x+1             -                      -            0      +                      +                     +

x-4            -                        -                     -                     -            0      +

\frac{(x-2)(x+3)}{(x+1)(x-4)}   +          0          -             ||        +         0        -            ||        +

from the board

=>    x ∈ [-3;-1) ∪ [2;4)

You might be interested in
.........................
Anastasy [175]
Y = 12x where x is the # of students and y is the # of adults

Or for every 12 students there's 1 adult
6 0
3 years ago
$15.30 divided by 15??????
alekssr [168]
The answer is 1.02 according to calculations
8 0
3 years ago
Read 2 more answers
3. Your friend has eight sweatshirts. Three sweatshirts are green, one is white, and
Sveta_85 [38]

Answer:

3/14

Step-by-step explanation:

P (B then B) = 4/8 x 3/7 or 1/2 x 3/7

6 0
3 years ago
Whats 94.732 x 26.75?
ddd [48]

Answer:

2534.081

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
?...............................
arsen [322]

Answer:

-2 ≤ n < 8

Step-by-step explanation:

_________________

5 0
3 years ago
Other questions:
  • I need help for this pleaseee
    11·2 answers
  • Crediting an account with a gift card of $60 positive or negative $60
    12·1 answer
  • Write equation in standard form if x-intercept is 5 and y-intercept is 3.
    9·1 answer
  • Which of the following is a perfect square<br> A. 13<br> B. 100<br> C. 127<br> D. 102
    11·1 answer
  • Customary capacity lesson 17.2 <br> How many times can 72 pt go into a gal
    10·1 answer
  • You have a bag which contains 15 slips of paper that are num- bered 1 through 15. You pull a piece of paper from the bag, do not
    12·1 answer
  • What are the values of a, b and c in the quadratic equation -2x2+4x -3=0
    7·2 answers
  • HELP ME PLEASE!!!!!!!
    15·2 answers
  • Find the area of the triangle
    15·1 answer
  • I WILL GIVE BRAINLIEST Hey can someone tell me simply HOW to come to this conclusion? im a bit confiused as to how, dont want to
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!