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
Alexandra [31]
2 years ago
14

The partial fraction decomposition of 9 x 11 6 x 2 23 x 21 can be written in the form of f ( x ) 2 x 3 g ( x ) 3 x 7 , where

Mathematics
1 answer:
svlad2 [7]2 years ago
6 0

Answer:

f(x) = -1

g(x) =6

\frac{-1}{2x + 3} + \frac{6}{3x + 7}

Step-by-step explanation:

The question is unreadable, however the real polynomial is:

The polynomial fraction is:

P = \frac{9x + 11}{6x^2 + 23x + 21}

And the decomposition is:

\frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}

The solution is as follows:

P = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}

Substitute the expression for P

\frac{9x + 11}{6x^2 + 23x + 21} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}

Expand the numerator of the polynomial

\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}

Take LCM

\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)*(3x + 7) + g(x)*(2x + 3)}{(2x + 3)(x + 7)}

Cancel out both denominators

9x + 11} = f(x)*(3x + 7) + g(x)*(2x + 3)

Represent f(x) as A and g(x) as B

9x + 11} = A*(3x + 7) + B*(2x + 3)

Open bracket

9x + 11} = 3Ax + 7A + 2Bx + 3B

9x + 11} = 3Ax + 2Bx+ 7A  + 3B

9x + 11} = (3A + 2B)x+ 7A  + 3B

By comparison:

3A + 2B = 9 ---- (1)

7A  + 3B =11 ---- (2)

Make B the subject in (1)

B = \frac{9 - 3A}{2}

Substitute B = \frac{9 - 3A}{2} in (2)

7A + 3(\frac{9 - 3A}{2}) = 11

Multiply through by 2

2*7A +2* 3(\frac{9 - 3A}{2}) = 11*2

14A + 3(9 - 3A) = 22

14A + 27 - 9A = 22

Collect Like Terms

14A - 9A = 22-27

5A = -5

A = \frac{-5}{5}

A = -1

Recall that:

B = \frac{9 - 3A}{2}

B = \frac{9 - 3 * -1}{2}

B = \frac{9 + 3}{2}

B = \frac{12}{2}

B = 6

A = -1 and B = 6

3A + 2B = 9 ---- (1)

7A  + 3B =11 ---- (2)

So:

f(x) = A

f(x) = -1

g(x) =B

g(x) =6

And the decomposition is:

\frac{-1}{2x + 3} + \frac{6}{3x + 7}

You might be interested in
Find the volume of a rectangular prism with the dimensions:
larisa86 [58]

Answer:

220

Step-by-step explanation:

V= whl = 5 · 11 · 4 = 220

8 0
2 years ago
Read 2 more answers
your sister is considering two different shapes for her garden. one is a square with side lengths of 3.5 meters, and the other i
In-s [12.5K]
The area of a square: (3.5m)²=12.25m²
The area of a circle: π*(2m)²=12.57m²
The circle shape of garden will give my sister more space to plant.
6 0
3 years ago
Which of the following lists of ordered pairs is a function? A.(2, 4), (3, 9), (4, 16), (5, 25) B.(0, 2), (4, 2), (0, –4), (4, –
marta [7]
A, is the answer because each input has one and only one output
3 0
3 years ago
Read 2 more answers
Kalynn plans to cut an 8 foot sandwich into pieces that are 1/2 foot long. How many pieces of the sandwich will she have after i
Kazeer [188]

Answer: 16

You divide 8 by 1/2 and you get 16 pieces

3 0
3 years ago
Need some help just can’t understand
allochka39001 [22]

Answer:

Positive I think

8 0
3 years ago
Read 2 more answers
Other questions:
  • Find two positive numbers whose ratio is 2:3 and whose product is 600.
    12·1 answer
  • By how many degrees did the direction of the boat change
    15·1 answer
  • Donavin has 5,734 baseball cards in his collection if each protective sheets does Donavin need? I NEED HELP
    11·1 answer
  • How do you reduce 2 1/32
    13·1 answer
  • The first step of Elimination in solving a system is to find opposites of one of the variable terms. Explain in your own words,
    11·2 answers
  • 3 1/2 x 2 3/4 divided by 1 1/2
    11·2 answers
  • A line intersects the points (13,-4) and (1, 12). Find the slope and simplify completely. Enter the correct symbol, + or - Slope
    11·1 answer
  • Simplify each expression by combining like terms. 3n - 1 + 8n +5
    13·1 answer
  • 4. Jake has m nails and twice as many bolts as nails. He buys another 20 nails and 30 bolts.
    11·1 answer
  • A man is 5 feet 9 inches tall. To find the height of a tree, the shadow of the man and the shadow of
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!