00:01
All right, guys.
00:01
So here we have a subtraction problem with two fractions where we don't have a common denominator yet.
00:06
So the first step in any problem like this is to get a common denominator.
00:11
And because we have binomials in the bottom, this variable plus a constant, the easiest way to get a common denominator is to multiply by the other denominator, because that guarantees that both denominators end up equal.
00:26
We'll multiply by the same value on the top of each of these fractions, so as to not change the value of our equation as a whole, because if we put the same thing as the top on the bottom, then we're only multiplying by one, which is always allowed.
00:39
So that's the first step in a problem like this, is to set it up, and then we simplify by doing this multiplication.
00:44
So let's start in the left side numerator.
00:46
We'll have to use the distribution, we'll have to use distribution multiplication, because we're multiplying 6x by a binomial here in 2x plus 3.
00:54
So we do 6x times 2x is 12x squared, plus 6x times 3 is 18.
01:04
So plus 18, or 18x rather, sorry.
01:07
So plus 18x.
01:08
And on the bottom, we're just going to leave our two binomials in a multiplied form, so as to keep the problem a little simpler.
01:16
2x plus 3, x plus 5.
01:20
And we'll do the exact same thing on the right side that we're subtracting.
01:23
So we know the denominator will be the same.
01:26
So we'll have 2x plus 3 and x plus 5.
01:32
And on the top, we'll do our multiplication again.
01:39
3 times x equals 3x plus 3 times 5 is 15.
01:44
So you have 3x plus 15.
01:47
All right.
01:48
So now that we have common denominators, we can simplify this down to one fraction with the same denominator in each side, or with the same denominator...