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
Eddi Din [679]
3 years ago
14

If x>2, then x^2-x-6/x^2-4=

Mathematics
1 answer:
Viefleur [7K]3 years ago
8 0
Consider the expression \frac{x^{2} -x-6}{ x^{2} -4}

To factorize the expression in the denominator we use difference of squares: x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)

To factorize x^{2} -x-6 we use the following method:

x^{2} -x-6=(x-a)(x-b)

where a, b are 2 numbers such that a+b= -1, the coefficient of x,

and a*b= -6, the constant.

such 2 numbers can be easily checked to be -3 and 2

(-3*2=6, -3+2=-1)

So x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)


 \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2}


\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}

for x>2

\frac{1}{x+2}\ \textless \  \frac{1}{2+2}= \frac{1}{4}

thus

for x>2, 

1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4}


Answer: 

for x>2

\frac{x^{2} -x-6}{ x^{2} -4} =  \frac{x+3}{x+2} \ \textless \  \frac{5}{4}, (but the expression is never 0)
You might be interested in
Which is greater 78.61 or78.6
ANTONII [103]

Answer:

78.61 is greater than 78.6.

Step-by-step explanation:

Adding a zero to 78.6, resulting in 78.60, makes it easier to compare 78.6 and 78.61.  78.61 is greater than 78.6.

7 0
3 years ago
1. Jack is 30 years old and Alice is 35 years old. What percent of Alice's age is Jack, rounded to the nearest tenth of a percen
Firlakuza [10]
The answer would be 57percent
4 0
3 years ago
A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a
USPshnik [31]

Answer:

The most appropriate inference procedure for the investigation is;

a. A linear regression t-interval for the slope

Step-by-step explanation:

Given that the slope of an horizontal line is zero, we have that there is no change in the y (dependent) variable when there is a change in the x-variable, therefore, it is important to find the true relationship between the two variables, 'x', and 'y'

The confidence interval of the slope is calculated and analyzed to determine if it excludes or includes, 0, such that, if the confidence interval exclude 0, then, it is unlikely that the slope is 0, therefore, there the relationship between the variables, 'x', and 'y' is significant

Therefore, a linear regression t-interval for the slope is most appropriate.

3 0
3 years ago
Hbdh What is u+ka= ba for a
balandron [24]
Minus ka from both sides
u=ba-ka
undistribute a
u=(a)(b-k)
diivde both sides by (b-k)
\frac{u}{b-k} =x
x= \frac{u}{b-k}

8 0
3 years ago
How are 2-D and 3-D objects related to each other in real world​
stich3 [128]

Answer:

You can see 2-D flat shapes on the faces of 3-D objects.

For example: You go to the store and you see a box,

the box has 6 faces. The bottom of the box is one of It's faces which is 2-D.

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Ritu started a business and borrowed a certain sum at 14% per annum for 1 year, the interest being compounded semi annually. If
    15·1 answer
  • Which of the following is a composite number?<br><br> A: 47<br> B: 91<br> C: 101<br> D: 131
    15·2 answers
  • F(x)=4x+13 and g(x)=10x-2,solve for (f+g)(x)
    14·1 answer
  • 1<br>9. By what rational number must<br>26<br>be divided to get<br>?<br>39​
    14·1 answer
  • Can you solve 2x+16 = 40
    12·2 answers
  • What is this plz help
    8·2 answers
  • 12 out of 30 tickets sold were early admission what percentage of tickets were early admission tickets
    12·1 answer
  • A pack of five basic solid T-shirts costs $29.95 in a store. The sales tax where they are sold is 7.75%. What is the unit cost o
    9·2 answers
  • Suppose that the populations of the United States and China both increase by 12 million people in one year. What would be the re
    6·1 answer
  • If the range of the function f(x) =5x + 8 is 18, find its domain.​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!