00:01
So we want to solve the equation x minus 2 divided by x squared plus 4x plus 3 is equal to 4 over 4x plus 4 minus 5 over x plus 3.
00:23
Well, we can factor the denominator on the left.
00:26
Let's see, x minus 2 divided by x plus 3 times x plus 1 is equal to 4.
00:37
I can factor out a 4 here.
00:40
4 times x plus 1 minus 5 over x plus 3.
00:48
Now i can cancel these 4s.
00:52
I just get a 1 in the denominator then.
00:55
And now i can, let's see here, multiply the right side by x plus 1 times x plus 3, and i can multiply the left then by the same thing to keep the equality intact, because what i do to the left i have to do to the right.
01:33
Alright, now since i have x plus 3 and x plus 1 in my denominator, i have to say that x cannot equal 1, or negative 1, and x cannot equal negative 3.
01:52
So now i can cancel that one with that one, and that one with that one.
01:57
So on the left i just have x minus 2 and on the right now i have well the first term was 1 over x plus 1 and i multiply that by x plus 1 times x plus 3 to x plus 1 cancel so i get just x plus 3 then minus 5 over x plus 3 times x plus 1 times x plus 3.
02:30
Well, that x plus 3 cancels with the denominator there.
02:35
So this is what i end up with...