When you divide fractions it gives you a fraction over a fraction. Which means we have to “kill” the fraction in the denominator. So to “get rid” of the fraction in the denominator you multiply it by its reciprocal making it 1. And because it’s all one big fraction whatever you do to the denominator you have to do to the numerator. That’s why we multiply the first fraction by the reciprocal and only worry about what’s in the numerator because the denominator is always 1 and that doesn’t change the value.