Partial Fraction Question: HELP with Polynomial Long Division

[n31son]

Homework Statement

x^2-x-13/(x^2+7)(x-2)

hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions.

I also know the answer is 2x+3/x^2+7 - 1/x-2 from an online calculator. but think I am missing something in the method to reach the answer.
any help appreciated thanks

 

[Mark44]

Homework Statement

x^2-x-13/(x^2+7)(x-2)

Unless you meant x² - x - (13/(x² + 7)(x - 2)), this should be written as (x^2-x-13)/((x^2+7)(x-2)).

hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions.

I also know the answer is 2x+3/x^2+7 - 1/x-2 from an online calculator. but think I am missing something in the method to reach the answer.

I doubt that is the answer. Maybe you meant (2x + 3)/(x² + 7) - 1/(x - 2). You should get in the habit of using parentheses around the numerator and denominator of your fractions.

any help appreciated thanks

No, you don't need to do polynomial long division first. The degree of the numerator is less than the degree of the denominator, so that division is unnecessary.

How did you break up the two fractions?

 

[n31son]

its defo the answer as it has been marked but returned for not showing working.
i may be wrong about the poly long division tho.

 

[n31son]

 

[Mark44]

What you show in post #4 is what you're starting with. When you decompose a rational expression such as that, you write it as a sum of two or more rational expressions.

For example, if you had to decompose x/(x² - 4), you would write it as A/(x - 2) + B/(x + 2), and you would solve for the constants A and B.

How are you going to break up your rational expression?