00:01
Let's determine the partial fraction decomposition of this rational expression.
00:06
That is x squared plus 9 divided by x -cube plus 5x squared.
00:10
So first, i'm going to rewrite this in the form of x -square plus 9.
00:14
I'm going to write the factor form of the denominator expression.
00:18
Here we have x -cube plus 5x squared.
00:21
And the g -c -f of this denominator is x -square.
00:24
So i factor out x -square.
00:26
When you do that, i get x -plus -5 as the second factor.
00:31
And so we have rewritten this rational expression in this form.
00:36
Now according to the partial fraction decomposition method, this can be written as a divided by since we have x squared, we write down x and then we put b divided by x squared with the exponent.
00:52
And then finally we write down c divided by the last factor that is x plus pi.
00:58
And so now we're going to focus only this equation.
01:01
To determine the constants a, b, and z.
01:06
Now, looking at this equation, the list common denominator of both sides is this expression, that is x squared times x plus 5.
01:16
So we are going to multiply both sides by the list common denominator.
01:20
And so we write x squared plus 9.
01:23
This is divided by x squared times x plus 5.
01:28
And we multiply this by x squared times x plus five and this equals on the right side also we multiplied by this is to common denominator that is x squared times x plus five and we have a divided by x plus b divided by x squared plus c divided by x plus five we are basically multiplying this factor so that we can remove the fraction on both sides.
02:03
We see that this x squared x squared getting canceled.
02:07
This x plus 5 also gets canceled with x plus 5.
02:10
So on the left side, we will have only x squared plus 9.
02:14
And this equals on the right side.
02:16
We are going to basically multiply or distribute this factor to all the terms inside the bracket...
