00:01
For this problem, we are given a table wherein the first one shows the rational expressions and the other table shows us the simplest forms.
00:13
To match them correctly, we are going to simplify each rational expression and find the simplest form from the second table.
00:25
So let's begin with the first expression there.
00:29
We have 4 over 9cd squared plus 3 over 5c squared d.
00:40
Now looking at the denominators, since we're adding, we need to find the least common denominator.
00:48
So the least common for the numbers will be 45.
00:52
And for the variable c it should be c squared and for the variable d it should be d squared.
01:01
So we need to make this denominator for each.
01:06
So we also have 45 c squared d squared for the other fraction.
01:11
Now to get this we need to multiply the first fraction by 5c and the other fraction you have to multiply that by 9d so that the first numerator will be 20c and the second numerator would be 27d.
01:41
Combining we get 20c plus 27d all over 45c squared d squared.
01:50
That means this will match number 3.
01:56
And for the next one, we have 2c over 4c squared minus 9 minus 3 over 2c plus 3.
02:10
Since this is subtraction, again we need to find a least common denominator.
02:15
Now, 4c squared minus 9 is the same as 2c minus 3 times 2c plus 3.
02:24
And then you have 2c in the numerator...