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
Reil [10]
3 years ago
14

Resolve into partial fractions​

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
3 0

Answer:

See below

Step-by-step explanation:

1)

\frac{11 + x}{(2 - x)(x - 3)}  =  \frac{A}{2 - x}  +  \frac{B}{x - 3}  \\  \\  \therefore \:  \frac{11 + x}{(2 - x)(x - 3)}  =  \frac{A(x - 3) +B(2 - x) }{(2 - x)(x - 3)}   \\  \\ \therefore \:  11 + x = Ax - 3A + 2B - Bx \\  \\  \therefore \: 11 + x = - 3A  + 2B  + Ax -  Bx\\  \\  \therefore \: 11 + x = - 3A  + 2B  + (A - B)x \\  \\ equating \: the \: like \: terms \: on \: both \: sides \\ A - B = 1 \\  \therefore \: A  =  B  +  1.....(1) \\  \\  -  3A  + 2B = 11....(2) \\  from \: eq \: (1) \: and \: (2) \\  - 3(B  +  1) + + 2B = 11 \\  \\ - 3B   - 3  + 2B = 11 \\  \\  - B = 11 + 3 \\  \\ B =  - 14  \\ A  =   - 14 +  1 =  - 13 \\  \\  \frac{11 + x}{(2 - x)(x - 3)}  =  \frac{ - 13}{2 - x}  +  \frac{ - 14}{x - 3} \\  \\ \frac{11 + x}{(2 - x)(x - 3)}  = -   \frac{ 13}{2 - x}   -  \frac{ 14}{x - 3}

2)

\frac{12x + 11}{x^2 +x - 6}

=\frac{12x + 11}{x^2 +3x-2x - 6}

=\frac{12x + 11}{x(x +3) -2(x +3)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}

\therefore 12x + 11 = A(x-2)+B(x+3)

\therefore 12x + 11 = Ax-2A+Bx+3B

\therefore 12x + 11 = Ax+Bx-2A+3B

\therefore 12x + 11 = (A+B) x-2A+3B

Equating like terms on both sides:

A + B = 12\implies A = 12-B... (1)

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

Solving equations (1) & (2), we find:

A = 5, B = 7

\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}

You might be interested in
HELP! "translate: the product of 8 and a number increased by 2 use x as the variable"
Bumek [7]

Answer:

variable is (<em> </em><em>x</em><em> </em><em>)</em>

<em>∆</em><em>product</em><em> </em><em>of</em><em> </em><em>8</em><em> </em><em>:</em>

<em>8</em><em> </em><em>x</em>

<em>∆</em><em>the</em><em> </em><em>number</em><em> </em><em>increase</em><em>d</em><em> </em><em>by</em><em> </em><em>2</em><em> </em><em>:</em><em> </em>

<em>8</em><em> </em><em>x</em><em> </em><em>+</em><em> </em><em>2</em>

<em>And</em><em> </em><em>we</em><em>'re</em><em> </em><em>done</em><em> </em><em>♥️</em>

3 0
3 years ago
Read 2 more answers
What set of Transformations are applied to parallelogram ABCD to create A'B'C'D'?​
bearhunter [10]

Answer:  a) reflected over x-axis and reflected over y-axis

<u>Step-by-step explanation:</u>

Reflection over the x-axis changes the sign of the y-coordinate

Z = (x, y)   →   Z'(x, -y)

Reflection over the y-axis changes the sign of the x-coordinate

Z' = (x, -y)   →   Z''(-x, -y)

A = (-4, 1)     →     A'' = (4, -1)    

B = (-3, 2)    →     A'' = (3, -2)

C = (-1, 2)     →     A'' = (1, -2)    

D = (-2, 1)     →     A'' = (2, -1)  

3 0
3 years ago
100 point will mark brainliest to first answer only
dimaraw [331]

Answer: no yes

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Estimate the area under the curve f(x) = x2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. An
BaLLatris [955]
1) split the range in three identical invervals of size [6 - 0] / 3 = 2

2) form three rectangles

2a) First rectangle: base 2, height f(2) = 2^2 + 1 = 5

     area 1 = base * height = 2 * 5 = 10

2b) second rectangle: base 2, height f(2+2) = 4^2 + 1 = 17

     area 2 = 2 * 17 = 34

2c) third rectangle: base 2 height f(4+2) = 6^2 + 1 = 37

     area 3 = 2*37 = 74

3) total area = area 1 + area 2 + area 3 = 10 + 34 + 74 =  118

3 0
2 years ago
Solve the equation<br><br> f(n)=10⋅2n for n = -2
Oksana_A [137]

Answer:

f(n)= -40.

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Rachael bought 4 shirts and some number of pants. Write an expression to show how many pieces of clothing she bought
    12·1 answer
  • Which of the following is not a correct statement or outcome for multiplying matrices?
    12·1 answer
  • A kid's pool is cylindrical and has a radius of 5 feet and a height of 2 feet. If a cubic foot holds about 7.48 gallons of water
    9·1 answer
  • Write as a single power of 8.<br> 8 to the power of 8<br><br> ÷<br> 8 to the power of 2
    7·1 answer
  • Whats the answer to this plz help​
    14·2 answers
  • A part is being machined. The starting thickness
    13·1 answer
  • What equation represents a line that when if graphed, passes through the points (0, -1) and
    13·1 answer
  • Find the length of side x in simplest radical form with a rational denominator.<br> X
    11·1 answer
  • 1.2 if a = -6, b = +4, c = -3 and d = -2 Calculate the value of :-
    12·1 answer
  • Can yall tell me what im doing wrong? for 50 points.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!