00:01
Find the partial fraction decomposition for minus 3 over x plus 2 times x plus 3 and use the result to find the following sum.
00:12
So here we let minus 3 over x plus 2 times x plus 3 equals a over x plus 2 plus b over x plus 3.
00:39
Okay, so minus 3 over x plus 2 times x plus 3 is equivalent to a times times.
00:45
X plus 3 over x plus 2 times x plus 3 plus b times x plus 2 over x plus 2 over x plus 3 okay with uniform denominator and for numerator i have a x plus 3 a plus bx plus 2 b over x plus 2 times x plus 3 okay so a plus b times x plus 3a plus 2b over x plus 2 times x plus 3.
01:54
Okay, by compare the left side and right side of the equality of the equation, we can set up the equation set.
02:03
Okay, since left side of the equation for the numerator, there's no term involved with x.
02:08
So a plus b here is 0.
02:12
And we have 3a plus 2b equals minus 3.
02:25
So we solve for a equals minus 3 and b equals 3.
02:45
So the partial fraction decomposition 4 minus 3 over x plus 2 times x plus 3 equals minus 3 times x plus 3 over x plus 2 times x plus 3 plus 3 plus 3 plus x plus 2 over x plus 2 times x plus 2 plus 3.
03:49
Sorry, here should be, we should go back to this one, okay, go back to this one.
03:56
So a over x plus 2, minus 3 over x plus 2, plus b over x plus 3.
04:03
So plus b over x plus 3.
04:07
Or you can switch the order, so we can factor out 3.
04:13
So i have 1 over x plus 3 minus 1 over x plus 2.
04:20
Now let's look at the original addition, expression, okay? here i made a little mistake for copy.
04:55
So let's try again...