Lesson 5ª

Multiplying and Dividing Algebraic Fractions. (Continued)

10.33  Calculate :

Solution:

10.34   Calculate:

Solution:
It is very important to notice where the ‘=’ sign is placed. By noticing this, we can know whether a middle term or an extreme term is missing.

In this exercise, (a – 1) doesn't have a denominator. To be able to have two extremes and two middles, we place 1 as a denominator to (a – 1) and we won't alter the value of the quotient.

THis way, we have two extremes and two middles. From this: …extreme products divided by middle products…

10.35 Calculate:

Solution:
By noticing the position of the ‘=’ sign, we find that we are missing an extreme ( denominator for ‘a – 1’). We write a 1 in its place:

10.36  Find the value of:

Solution:

We start at the end:

and we write this value:

We find that we are missing a middle term; the one that should go under 1. As always, we write a 1 where the term is missing:

10.37  Calculate:

Solution:

10.38   Calculate the quotient:

Solution:

There is a factoring product whose application is not as frequent as the ones we have studied so far:

10.39   Calculate: