See Above
Answers
Formula :-
❍On substituting 'x = - 0' in equation (2), we get :-
❍On substituting 'x = 1' in equation (2), we get :-
❍Now, substitute the values..
⠀⠀⠀ ━━━━━━━━━━━━━━━━━━━⠀
- Partial fraction decomposition is the breaking down of a rational expression into simpler parts. It is the opposite of adding rational expressions. When adding two rational expressions, there has to be a common denominator.
⠀⠀⠀ ━━━━━━━━━━━━━━━━━━━⠀
To Do :-
- To resolve into partial fractions .
SolutioN :-
The process of expressing a proper fraction as a sum of two or more proper fraction is called resolving it into Partial Fractions.
Here the fraction given to us is ,
Here the degree of denominator is greater than the degree of numerator . Hence the fraction is Proper Fraction and we can resolve it into Partial fractions .
• Assume that ,
Comparing the co - efficients of x² on both sides of the equation we have ,
Let us assume a fraction ( proper ) ,
T Y P E - 1 :-
When g(x) has non repeated linear fractions only , then there exists a corresponding partial fraction in the form of
________________________________
T Y P E - 2 :-
When g(x) has some repeated linear factors and the remaining are non repeated linear factors .
Then for corresponding linear factor ,
Then for corresponding non-linear repeated Fractions ,
For example of this type refer to the attachment.
________________________________
T Y P E - 3 :-
When g(x) contains non - repeated non - reducible factors in form of a quadratic equation. that is px² + qx + c . The Partial Fraction for this type is ,
where p , q , A and B belong to Real Numbers .