1st Year Math Chapter 5

Hello Students!
This post is to explain completely Chapter 5 of 1st Year Math that is PARTIAL FRACTIONS.
First of all I want to give an introduction of what partial fractions actually are. You have already done the process of combining more than one fractions by simply making the denominators common and then simplify it.

Now we have to learn how to convert a combined fraction into its partial fractions.

First of all we have to check whether the fraction that is given in the question is proper or not.

Remember, a proper fraction is that in which the degree of the numerator is less than the degree of the denominator. Degree of a polynomial is the maximum power of the variable involved in it. If it is a proper fraction, then we will proceed as follows. I am sharing a picture of the solved question of Ex. 5.1.

The method of putting the values to make one unknown thing zero and finding the other is very useful but it works only when the denominator is having factors that are linear and non - repeated. We will discuss some complex problems in Ex. 5.2, 5.3 & 5.4.

Right now I want to discuss the case when the given fraction is not proper. First we have to make it proper in that  case.

You should remember that for an improper fraction, that is the case when the degree of the numerator is not less than the denominator,

Dividend ÷ Divisor = Quotient + Remainder ÷ Divisor.

So right now I want to share the solution of Q.2 of Ex. 5.1 which is a good example of how to resolve an improper fraction into its partial fractions.
Q.2:-

Q.7:-

Hope it would be a very helpful post for all my 1st year math students in particular and all math students in general.

Have a nice time.

I will continue this to explain the further exercises of this chapter. Till then, take care!

Regards,

Adeel Lutf

Principal

The British Cambridge