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
const2013 [10]
2 years ago
12

What is the partial fraction decomposition of StartFraction 8 x + 19 Over (x + 8) (x minus 1) EndFraction? StartFraction 3 Over

x + 8 EndFraction + StartFraction 5 Over x minus 1 EndFraction StartFraction 5 Over x + 8 EndFraction + StartFraction 3 Over x minus 1 EndFraction StartFraction negative 3 Over x + 8 EndFraction + StartFraction 11 Over x minus 1 EndFraction StartFraction 11 Over x + 8 EndFraction + StartFraction negative 3 Over x minus 1 EndFraction
Mathematics
1 answer:
hoa [83]2 years ago
6 0

The partial fraction decomposition is \frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}

<h3>How to determine the decomposition?</h3>

The fraction is given as:

\frac{8x + 19}{(x + 8)(x - 1)}

Split the fraction as follows:

\frac{8x + 19}{(x + 8)(x - 1)} = \frac{A}{x + 8} + \frac{B}{x - 1}

Take the LCM

\frac{8x + 19}{(x + 8)(x - 1)} = \frac{Ax -A + Bx + 8B}{(x + 8)(x -1)}

Cancel the common factors

8x + 19 = Ax - A + Bx + 8B

By comparison, we have:

Ax + Bx = 8x

-A + 8B = 19

This gives

A + B = 8

-A + 8B = 19

Add both equations

9B = 27

Divide by 9

B = 3

Substitute B = 3 in A + B = 8

A + 3 = 8

Solve for A

A = 5

So, we have:

\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}

Hence, the partial fraction decomposition is \frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}

Read more about partial fraction at:

brainly.com/question/12783868

#SPJ1

You might be interested in
Angelica is currently 13 years old she is 2 years older than her brother. Write an equation to represent the situation.Solve ur
sdas [7]

Answer:

Therefore,

x+2=13 .......Equation

Angelica's Brother's age is 11 years old.

Step-by-step explanation:

Given:

Let the current age of Angelica's Brother be 'x' years old

Angelica's current age is 13 years old,

According to given condition,

Therefore the Equation will be,

x+2=13

On solving this equation we get

x=13-2=11\\\\x=11\ years

Therefore,

Angelica's Brother's age is 11 years old.

Therefore,

x+2=13 .......Equation

Angelica's Brother's age is 11 years old.

6 0
3 years ago
How many solutions for -2(3-x) = x+6
lora16 [44]

Answer:

x=12

Step-by-step explanation:

8 0
3 years ago
ASAP PLZ which properties are present in a table that represents an expotential function in the form y=b^x when b&gt;1?
sdas [7]

Answer:

I and IV

Step-by-step explanation:

4 0
3 years ago
What is 150/5? I need help asap plz
Readme [11.4K]
If your just doing 150 divided by 5 then the answer would be 30
8 0
3 years ago
Read 2 more answers
Somebody help me please<br> I have to find the midpoint of the line
nika2105 [10]

Answer:

i think u mean the y axis which would be -2

6 0
2 years ago
Other questions:
  • Amelia lost her credit card one day while on vacation. She reported the loss to the credit card company the next day. However ,
    6·1 answer
  • The sum of 18 +45 is a multiple of which sum?
    12·1 answer
  • Miss Rodriguez is purchasing trophies for each child that plays Little League she wants to spend no more than seven dollars per
    11·1 answer
  • Select the graph of the solution. Click until the correct graph appears.<br><br> | x | = 1
    14·2 answers
  • Betsy spent 36 days traveling in europe how many weeks and days did betsy travel in europe
    14·2 answers
  • What is 9×10^4 equal to
    15·1 answer
  • If m&lt;9=97 and m&lt;12=114, find each measure.
    11·1 answer
  • Vector V is in standard position and makes an angle of 50° with the positive x-axis. Its magnitude is 15. Write V in component f
    11·1 answer
  • Can anyone help me with this?
    15·2 answers
  • LOOK AT THE PICTURE BLOW
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!