Partial fractions of irreducible quadratic factors. Hi guys, today I will discuss partial fractions of irreducible quadratic factors. Have a look!!
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Solved examples of partial fractions of irreducible quadratic factors
Now here comes my first example.
Write the following expression into partial fraction form:
Here the given expression is: . As I can see, I can’t factorize the denominator further. So this is an example of an expression with irreducible quadratic factor. Now my task is to get the partial fraction of this expression.
Also, I can rewrite this expression as
where and are constants.
Next, I’ll simplify the right-hand side of the equation. So this gives
Then I’ll simplify it a bit more to get
At the end, it becomes
Now the denominator of both the left-hand side and right-hand side are the same. So I can compare the numerators of both sides. And this gives
Next, I compare the coefficients of on both sides to get
Then I compare the coefficients of on both sides to get
And this means
Next, I’ll substitute this value of in equation (3) to get
So this means
Finally, I’ll substitute in equation (1) to get
So this means
Therefore I can say is the partial fraction form of .
And this is the solution to the given example.
Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!