Find out the partial fraction decomposition, Algebra

Find out the partial fraction decomposition of each of the following.

8x2 -12/( x( x2 + 2 x - 6)

Solution

In this case the x which sits in the front is a linear term as we can write it as, x= x + 0 and thus the form of the partial fraction decomposition is,

8x2 -12 /x( x2 + 2 x - 6) =  A /x +      Bx+ C/ x2 + 2 x - 6

Now we'll utilizes the fact that the LCD is and add the two terms together,

8x2 -12 / x( x2 + 2 x - 6) = A ( x2 + 2 x - 6 )+ x ( Bx+ C ) / x(x2 + 2 x - 6)

After that, set the numerators equal.

                             8x2 -12 = A ( x2 + 2 x - 6 )+ x ( Bx+ C )

This is where the procedure changes from the previous example.  We could select x= 0 to obtain the value of A, although that's the only constant which we could get by using this method and thus it just won't work all that well here.

What we have to do here is multiply the right side out & then gather all the like terms as follows,

8x2 -12 = Ax2 + 2 Ax - 6 A + Bx2 + Cx

8x2 -12 = ( A + B )x2 + ( 2 A + C ) x - 6 A

 

Now, we have to choose A, B, and C hence that these two are equal. This means that the coefficient of the x2 term on the right side will need to be 8 as that is the coefficient of the x2 term on the left side.  Similarly, the coefficient of the x term on the right side has to be zero as there isn't an x term on the left side.  At last the constant term on the right side has to be -12 as that is the constant on the left side.

Generally we call these setting coefficients equivalent & we'll write down the following equations.

A + B= 8

2 A + C = 0

-6 A= -12

Now, we haven't talked regarding how to solve systems of equations still, although this is one that we can do without that knowledge. We can solve out the third equation directly for A to obtain that A = 2 .  Then we can plug this into the first two equations to obtain,

2 + B = 8                 ⇒            B = 6

2 ( 2) + C = 0         ⇒  C = -4

Thus, the partial fraction decomposition for this expression is,

8x2 -12/ x( x2 + 2 x - 6) =  (2/x)+(6x-4)/ ( x2 + 2 x - 6)

Posted Date: 4/8/2013 3:05:05 AM | Location : United States







Related Discussions:- Find out the partial fraction decomposition, Assignment Help, Ask Question on Find out the partial fraction decomposition, Get Answer, Expert's Help, Find out the partial fraction decomposition Discussions

Write discussion on Find out the partial fraction decomposition
Your posts are moderated
Related Questions

what is the answer to y is greater than 3x-l and y is less than x+2

Coordinates for the point  The listed first number is the x-coordinate of the point and the second number listed is the y-coordinate of the point. The ordered pair for any spec

Example :   Use the quadratic formula to solve following equation.                            x 2 + 2x = 7 Solution Here the important part is to ensure that before we b

.1.Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). ?Now le

How to do x+y+z?

Nel skates at 18 mph and and Christine skates at 22 mph if they can keep up that pace for 4.5 hours how far will they be a part at the end of the time

where and how does the letter a and b where and how do u use them

Use the infomation beow tassess how much money Dave and Jane will be able to give to charity. They plan toma them in two sizes, small and large. Dave will carve them from wood. Sma