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
andreyandreev [35.5K]
2 years ago
15

Evaluate the difference quotient for the given function. Simplify your answer.

Mathematics
1 answer:
nasty-shy [4]2 years ago
4 0

I suppose you mean

f(x) = \dfrac{x+5}{x+1}

Then

f(3) = \dfrac{3+5}{3+1} = \dfrac84 = 2

and the difference quotient is

\dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5}{x+1}-2}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5-2(x+1)}{x+1}}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{-x+3}{(x+1)(x-3)} \\\\ \dfrac{f(x)-f(3)}{x-3} = \boxed{-\dfrac{x-3}{(x+1)(x-3)}}

If it's the case that <em>x</em> ≠ 3, then (<em>x</em> - 3)/(<em>x</em> - 3) reduces to 1, and you would be left with

\dfrac{f(x)-f(3)}{x-3}\bigg|_{x\neq3} = -\dfrac1{x+1}

You might be interested in
How do i turn 24% into a fraction
PolarNik [594]
You can remove the % sign if you divide the number by 100:

\frac{24}{100}


This is because % is defined as 1/100, and the name (per-cent) actually meant this originally!
we can also simplify it: let's divide it by 4:

\frac{6}{25}




7 0
3 years ago
If Dylan buys a book that is 25% off, what percent of the original price does Dylan pay?​
Schach [20]
Dylan will pay 75% of the original price.
5 0
2 years ago
Read 2 more answers
Through: (3, 4), slope = -2​
sineoko [7]

Answer:

y = -2x - 2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Points: (3, 4)

Slope: -2

y = -2x + b

4 = -2 ( 3 ) + b

4 = -6 + b

b = -2

y = -2x - 2

8 0
3 years ago
Read 2 more answers
What is the solution to
Brums [2.3K]

Answer:

x\geq12

Step-by-step explanation:

8 0
3 years ago
What is the volume of this prism ???
pshichka [43]

Answer:

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Rose has 18 tulips and 20 daffodils. She wants to make identical bouquets using all the flowers. What is the greatest number of
    8·1 answer
  • How many solutions does 2x-15≤31
    15·1 answer
  • Write 863.141 in expanded form
    11·1 answer
  • Which division problem would have an estimated quotient of 15 if the divisor and dividend were rounded to the nearest whole numb
    14·2 answers
  • Help me please <br> I’ll make it brainliest !!!!!
    14·1 answer
  • WHAT IS THE RANGE AND DOMAIN. NEED HELP PLEASE.
    15·1 answer
  • Big burger is offering a value meal that includes a burger, and two side items such as fries, salad or drink. each if the side i
    7·1 answer
  • Solve the system of equations. (HINT: use the elimination method)<br> 7x+4y=2<br> 9x-4y=30
    10·1 answer
  • Stacy's dining room is 6 yards wide and 6 yards long. Stacy wants to install a new wood floor. It will cost $7.09 per square yar
    10·2 answers
  • What is the local tax deducted for $562 biweekly with 2 1/2% tax? $14.05 $ $21.10 $28.10 $140.50​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!