00:01
To evaluate x over x raised to the fourth power minus 2x squared minus 3, note that we can rewrite x over x to the fourth minus 2x squared minus 3 into x over x squared minus 3 times x squared plus 1.
00:24
So this is equal to ax plus b over x squared minus 3 plus cx plus d all over x squared plus 1.
00:36
And then we're going to multiply this by the lcd x squared minus 3 times x squared plus 1.
00:44
It's going to give us x equal to ax plus b times x squared plus 1 plus cx plus d times x squared minus 3.
00:56
And then we will expand this.
00:59
We get x equal to ax cubed plus ax plus bx squared plus b plus cx cubed minus 3cx plus dx squared minus 3d.
01:19
We combine similar terms, that's x equal to a plus c times x cubed plus b plus d times x squared plus a minus 3c times x and then plus b minus 3d.
01:41
So comparing the coefficients at the left and at the right side, we can form equations.
01:47
For x cubed, we have a plus c equal to 0.
01:51
For x squared, we have b plus d equal to 0.
01:56
For x, we have a minus 3c equal to 1.
02:01
And for the constant term, since we don't have it at the left side, that's b minus 3d equal to 0.
02:09
From here, we can already solve for a.
02:12
A is equivalent to negative c...