Final answer:
The student's question involves decomposing the function 1/(x² -5x+6) into linear factors by first factoring the quadratic denominator, then using partial fractions to find the coefficients that will simplify the expression.
Step-by-step explanation:
The student has asked about the Linear Factors Decomposition of the function f(x) = 1/(x² -5x+6). To find the linear factors, we first need to factor the quadratic denominator. The denominator factors into (x-2)(x-3), allowing us to decompose the function into partial fractions as follows:
- Set up the equation ²1/(x-2)(x-3)² = A/(x-2) + B/(x-3)
- Find the values of A and B by multiplying both sides by the denominator and setting up equations for x that eliminate one of the denominators at a time.
- Solve the system of equations to find A and B.
Once A and B are found, the original function can be expressed as the sum of two simpler fractions which are easier to integrate or differentiate if required.