Question

Find the sum of partial fractions for .1/(x-1)(x+2)

Answer 1

To find the sum of partial fractions for 1/(x-1)(x+2), we first express it as A/(x-1) + B/(x+2) and then find the values of A and B.

Step-by-step explanation:

To find the sum of partial fractions for 1/(x-1)(x+2), we assume the equation can be broken into the form A/(x-1) + B/(x+2). Our next step is to find the values of A and B that will satisfy the equation. We multiply both sides by the common denominator (x-1)(x+2) to avoid fractions and solve for A and B by equating coefficients or plugging in suitable values for x that simplify the equation.

Once we have the values of A and B, we can express the original fraction as the sum of two simpler fractions. Let's illustrate this step by step:

1. 
   
3. Multiply both sides of the equation by the common denominator: (x-1)(x+2) to obtain 1 = A(x+2) + B(x-1).
4. 
   
6. Expand and simplify the equation to find A and B.
7. 
   
9. Write the final sum of partial fractions using the found values of A and B.

By solving this algebraic equation, we will obtain our final sum of partial fractions.