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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)

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Step-by-step explanation:

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What is 11 1/2 + 10 11/16=
ahrayia [7]

Hey!



To solve this equation, we must first convert the mixed numbers into improper fractions. To do that we'll multiply the denominator by the whole number and add the total to the numerator.


<em>Original Equation :</em>

11\frac{1}{2} + 10\frac{11}{16} = ?


<em>New Equation {Converted Mixed Numbers Into Improper Fractions} :</em>

\frac{23}{2} + \frac{171}{16} = ?


Now that we've successfully changed our equation, we'll move onto the next step. Next we'll have change the fractions one more time so that the denominators are the same. To do that we'll multiply two by eight to get sixteen. We'll also be multiplying the top portion of the fraction by eight, because whatever you do to the bottom must also be done to the top; And vise versa.


<em>Fraction Conversion :</em>

\frac{23*8}{2*8} = \frac{184}{16}


So, now that we have our new fraction we can go ahead and plug that into our equation so we can start adding. Remember, we don't add the denominators, just the numerators.


<em>Old Equation :</em>

\frac{23}{2} + \frac{171}{16} = ?


<em>New Equation {Input New Fraction With Common Denominator} :</em>

\frac{184}{16} +\frac{171}{16} = ?


<em>Solution {New Equation Solved} :</em>

\frac{355}{16}


Now I'm not exactly sure how your instructor will accept your answer, but most prefer the final answer to be in the simplest form. In other words, they don't want it in the form of an improper fraction. They'd most likely rather have it as a mixed number.


<em>New Solution {Converted to a Mixed Number} :</em>

22\frac{3}{16}


Since the fraction cannot be simplified anymore, this should be our final answer.

<em>So, this means that the answer to the equation is </em> 22\frac{3}{16}.


Hope this helps!



- Lindsey Frazier ♥

5 0
3 years ago
Read 2 more answers
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katovenus [111]

Answer: x-9

Step-by-step explanation: because x is lower than Tony's money you would have to subtract x (Michelle's money) from Tony's ( which is 9)

This is why the answer would be X-9

Hope this helps!!!

8 0
1 year ago
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