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Ask Your Teacher Write out the form of the partial fraction decomposition of the function (See Example). Do not determine the numerical values of the coefficients. (If the partial fraction decomposition does not exist, enter DNE.) (a) x x2 + x − 20 (b) x2 x2 + x + 2

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Answer:

Step-by-step explanation:

Given to ask the Teacher Write out the form of the partial fraction decomposition of the function

It is not necessary to find the coefficients

For decomposition of partial fractions the necessary condition is that the denominator should be in a position to be factored into atleast two factors.

Then only partial fraction is possible otherwise not.

Here

a) [tex]\frac{x}{x^2+x-20}[/tex]

Denominator = [tex]x^2+x-20\\=(x+5)(x-4)[/tex]

So this can be resolved into partial fractions as

[tex]\frac{x}{x^2+x-20}=\frac{A}{x+5}+ \frac{B}{x-4}[/tex]

b) Here given

[tex]\frac{x^2}{x^2+x+2} \\=\frac{x^2+x+2-x-2}{x^2+x+2} \\=1-\frac{x+2}{x^2+x+2}[/tex]

But denominator cannot be factored

So cannot be decomposed into partial fraction

DNE

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