All categories

3 years ago

Write the form of the partial fraction decomposition of the rational expression.

Mathematics

1 answer:

balu736 [363]3 years ago

3 0

Answer:

x+7x2+3x+2=6x+1+−5x+2

Step-by-step explanation:

Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)

The form of the partial fraction decomposition is

x+7(x+1)(x+2)=Ax+1+Bx+2

Write the right-hand side as a single fraction:

x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)

The denominators are equal, so we require the equality of the numerators:

x+7=(x+1)B+(x+2)A

Expand the right-hand side:

x+7=xA+xB+2A+B

Collect up the like terms:

x+7=x(A+B)+2A+B

The coefficients near the like terms should be equal, so the following system is obtained:

{A+B=12A+B=7

Solving it (for steps, see system of equations calculator), we get that A=6, B=−5

Therefore,

x+7(x+1)(x+2)=6x+1+−5x+2

Answer: x+7x2+3x+2=6x+1+−5x+2

You might be interested in

**who can help me**

Furkat [3]

Answer:

Step-by-step explanation:

4 0

3 years ago

What is the remainder to x^3+4x^2+x-6 divided by (x-1)

serg [7]

$x^3=x^2\cdot x$ , and $x^2(x-1)=x^3-x^2$ . This gives a remainder of

$(x^3+4x^2+x-6)-(x^3-x^2)=5x^2+x-6$

$5x^2=5x\cdot x$ , and $5x(x-1)=5x^2-5x$ . This gives a new remainder of

$(5x^2+x-6)-(5x^2-5x)=6x-6$

$6x=6\cdot x$ , and $6(x-1)=6x-6$ . This gives a new remainder of

$(6x-6)-(6x-6)=0$

and so there is no remainder.

###

Quicker method: Use the polynomial remainder theorem, which says the remainder upon dividing a polynomial $p(x)$ by $x-c$ is $p(c)$ . Here we have

$p(x)=x^3+4x^2+x-6$

$c=1\implies p(c)=1+4+1-6=0$

5 0

4 years ago

The following table shows the number of innings pitched by each of the Greenbury Goblin's starting pitchers during the Rockbotto

Sedaia [141]

Answer:

Step-by-step explanation

i can help u, but what are the numbers

7 0

4 years ago

Read 2 more answers

Consider the work shown for 94÷3. What does 31 represent?

alina1380 [7]

I think it represents the answer to the problem.

6 0

3 years ago

Read 2 more answers

EDIT// answer below thank for the help -.-

HACTEHA [7]

Step-by-step explanation:

Move it it up 4 and then find your x intercepts.

Find the x intercepts.

$-x^2 + 4 = 0$

Move the 4 over to the right

$-x^2 = -4$

Divide out the -

$\frac{-x^2}{-} = \frac{-4}{-}$

$x^2 = 4$

Take the square root of each side

$\sqrt{x^2} = \pm \sqrt{4}$

$x = \pm \sqrt 2$

Our x intercepts are at (-2,0) (2,0)

8 0

4 years ago