00:01
In this question, we want to break down this rational fraction into its partial fraction.
00:06
Let's go through the three points.
00:09
Is this fraction improper? improper would mean the numerator highest order or highest degree.
00:16
It's greater or equals to the denominator highest degree.
00:19
Now in this case, the numerator has degree zero and the denominator highest degree is two.
00:26
So it is a proper fraction because the numerator power, highest power, is less than the denominator highest power.
00:37
Now in any case, if your fraction is improper, please perform long division first.
00:44
Second point, can the denominator be factorized? in this case, yes, it can be factorized.
00:50
So let's do so.
00:54
Third point, are there repeated factors? in this case, no.
00:59
Repeated will look like this.
01:03
X squared is the repeated factor.
01:04
But in this case, in our question, no, we do not have any repeated factors.
01:09
This will affect the way we decompose it.
01:12
So now, let's use me over x plus over x plus 1.
01:23
Now what do we put in a numerator? numerator will always be one power less than the denominator.
01:29
So this will be a constant because the numerator is linear, plus b, also constant because its denominator is linear.
01:39
So now we're going to multiply every term by the common denominator, which will be x, x plus 1, every term.
01:54
So obviously, this is cancelled.
01:57
Here, only x is cancelled, and here x plus 1 is cancelled...