Equivalent form of the partial fractions is:







By the cover up method;
when
From equation
From equation (2),

Equivalent form of the partial fractions is

By the cover method;
When
From equation (1)
From equation (3)
Hence

Equivalent on of partial fractions is
.
The constants  and  can be obtained by the cover up metiod.
When
When
To get  we can substitute  and solve for

Equivalent on of partial fractions is
.
The constants  and  can be obtained by the cover up metiod.
When
When
To get  we can substitute  and solve for

Equivalent form of the partial fraction is

Here we can only get  by the cover up method thus:
To get  and  we can proceed thus


At this point you may expand and compare coefficients or you substitute simple values of , form equations and then solve them.
When  we have
Putting  we have

When  we have
Putting  we have

Equation
From equation (2)

Equivalent form of partial fraction is
.
In this case we can get the constants  and  by cover up method but not .
When there are repeated factors, the cover up method gives the constant which has the higher or highest power at the denominator.
When
When
Hawing obtained the values of  and , we use any value of  not already used to solve for . For example let  then we get

Here we see that the degree of the numerator and denominator is the same. So we carry out long

Therefore, we can now say

We now express  in partial fractions thus

When
When

We can write  as

Equivalent form of the partial fraction is

By the cover up metliod
When
when

Equivalent form of partial fraction is

By the cover up method when

In the case of linear factors we can solve by two methods.
Method 1
Let

Comparing the coefficient and the constants we have:

From equation 
Substituting  in  we have

Thus

Method 2: The cover up method.
This method is strictly limited to linear factors and to a lesser extent to repeated factors at the denominator.
To get the constant , we equate the denominator of A to zero ie. , we get . Then we Substitute  in the left hand side; covering the factor under , that is .
Hence
Similarly to get  we put  or . We substutute  in the LHS, covering .
Thus
Again we see that