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Write the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients. 1/(x-1)(x 9)

User Apex
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1 Answer

7 votes

Answer:


(A)/((x-1)) + (B)/((x-9))

Explanation:

Given the expression
(1)/((x-1)(x-9)), we are to write the expression as a partial fraction. Writing as a partial fraction means rewriting the expression a s a sum of two or more expression.

Before we will do this we will need to check the nature of the function at the denominator whether it is linear, quadratic or a repeated function. According to the question, the denominator at the denominator is a linear function and since it is a linear function, we can separate both linear function without restriction as shown;


(1)/((x-1)(x-9)) = (A)/((x-1)) + (B)/((x-9)) where A and B are the unknown constant which are numerical values.

User Vahagn Nahapetyan
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