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
Ivan
3 years ago
7

Write the partial fraction decomposition fro the ration expression below

Mathematics
1 answer:
zlopas [31]3 years ago
6 0
\dfrac{5x-2}{(x-1)^2}=\dfrac a{x-1}+\dfrac b{(x-1)^2}
5x-2=a(x-1)+b

Since 5x-2=5x-5+3=5(x-1)+3, it follows that a=5 and b=3, so

\dfrac{5x-2}{(x-1)^2}=\dfrac5{x-1}+\dfrac3{(x-1)^2}

\dfrac{x^3+x^2+x+2}{x^4+x^2}=\dfrac{x^3+x+x+2}{x^2(x^2+1)}=\dfrac ax+\dfrac b{x^2}+\dfrac{cx+d}{x^2+1}
x^3+x^2+x+2=ax(x^2+1)+b(x^2+1)+(cx+d)x^2
x^3+x^2+x+2=(a+c)x^3+(b+d)x^2+ax+b

When x=0, you find that b=2. It's also clear that a=1. So the remaining constants must be 1+c=1\implies c=0 and 2+d=1\implies d=-1, and so you get

\dfrac{x^3+x^2+x+2}{x^4+x^2}=\dfrac1x+\dfrac2{x^2}-\dfrac1{x^2+1}
You might be interested in
A sequence is defined by the equation a1=50 and an=an-1+(-4) what is term a5?
ZanzabumX [31]

Answer:

Step-by-step explanation:

an=an-1+(-4)

a2 = a1 + (-4) = 50 - 4 = 46

a3 = a2 - 4 = 46 - 4 = 42

a4 = a3 - 4 = 42 - 4 = 38

a5 = a4 - 4 = 38 - 4 = 34

6 0
2 years ago
HELPP plz I will give BRAINLIST <br><br> EXPLAIN HOW TO GET STEPS IN WORDS PLZ
Evgesh-ka [11]

Answer:

this is school work

Step-by-step explanation: sorry but you gotta figure this out yourself.

but, the thing is that you should figure out the stuff inside the (these -->) then figure out the rest step by step like this, x= what then try to understand y= what, then use them to answer the problem.

and if its like this 1(4x + 5y) that mean that 9xy times 1 is your answer, this is an example.

8 0
3 years ago
WILL GIVE BRAINLIEST!!!!!!!!
bulgar [2K]

I think the answer could be 10 or even 12

3 0
2 years ago
The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph
ra1l [238]

Answer:

c.

Step-by-step explanation:

i did it

6 0
3 years ago
A bird flies at a top speed of 20,000 meters per hour. The bird flies 30,000 meters without stopping. a. For how many hours did
bazaltina [42]

Answer:

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • If a country's debt-to-GDP ratio if currently 50% and its debt is expected to grow from $40 trillion to $50 trillion in the next
    5·1 answer
  • Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollar
    11·2 answers
  • How do u turn 2.15 to a fraction
    8·2 answers
  • Please help with this problem! Will give Brainliest! Geometry. Find the area of the figure
    5·2 answers
  • Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ x + 2. He instructed Han to add a second inequality to the graph th
    13·2 answers
  • Helpp il mark u as Brainlist​
    14·2 answers
  • I NEED HELP!!! PLEASE! PLEASE! PLEASE! ASAP!
    13·1 answer
  • Simultaneous EQUATION 3x+2y=16 2x+y=9 PLS HELP I need answer quickly
    6·1 answer
  • PLEASE HELPPPPPPPPPP IM RLLY STUCK
    5·2 answers
  • Please help!<br><br> Are these triangles similar?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!