00:01
Hi, in this question given that minus 9 x squared plus 7x minus 4 divided by x cube minus 3 x squared minus 4x.
00:12
We need to solve this by using partial fraction method.
00:16
So it can be written as minus 9 x squared plus 7x minus 4 the whole divided by on taking x commonly outside in the denominator.
00:25
Then we get x into x squared minus 3x minus 4 which is equal to minus 9 x squared plus 7x plus 4 divided by x into on further simplifying this we get x plus 1 into x minus 4 therefore we can write it as minus 9 x squared plus 7x plus 4 divided by x into x plus 1 into x minus 4.
00:56
Equals a divided by x plus b divided by x plus 1 plus c divided by x minus 4.
01:04
We need to find the values of a, b, c, which can be written as a into x plus 1 into x minus 4 plus b into x into x minus 4 plus b into x into x minus 4 plus c into x into x plus 1.
01:20
The whole divided by x into x plus 1 into x minus 4 which is equal to minus 9 x square plus 7 x plus 4 the whole divided by x into x plus 1 into x minus 4 here both the denominator or cancel each other so that we have to equate the numerator so that we get a into x plus 1 into x minus 4 plus b into x into x minus 4 plus c into x into x plus 1 which is equal to minus 9 x squared plus 7x plus 4.
02:01
Here we need to find the values of a, b and c.
02:05
For that purpose first we need to substitute x equal to 0 so that we get a into 1 into minus 4.
02:13
All the other terms become 0 which is equal to minus 4 which implies minus 4 a equals minus 4.
02:20
Therefore, a equals 1.
02:24
Next, we need to find the value of b...