Question

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)

Answer 1

Answer:

$\frac{A}{(x-1)} + \frac{B}{(x-9)}$

Step-by-step explanation:

Given the expression $\dfrac{1}{(x-1)(x-9)}$, 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;

$\dfrac{1}{(x-1)(x-9)} = \frac{A}{(x-1)} + \frac{B}{(x-9)}$ where A and B are the unknown constant which are numerical values.