Question

Express the rational function as a sum or difference of two simpler rational expressions:

A) Factorization
B) Integration
C) Differentiation
D) Trigonometric substitution

Answer 1

To express a rational function as a sum or difference of two simpler rational expressions, we need to factorize the numerator and denominator and then rewrite the rational function in terms of the factored expressions. This can be done using the process of partial fraction decomposition.

Step-by-step explanation:

To express a rational function as a sum or difference of two simpler rational expressions, we need to factorize the numerator and denominator and then rewrite the rational function in terms of the factored expressions. This can be done using the process of partial fraction decomposition.

1. Factorize the numerator and denominator of the rational function.
2. Write the rational function as a sum or difference of simpler rational expressions with each factored expression as the denominator.
3. Find the unknown coefficients by equating the numerators of the rational expressions.
4. Combine the rational expressions and simplify if needed.

For example, if we have the rational function (3x + 2) / (x^2 - 4x + 4), we can factorize the denominator as (x - 2)^2. Then, we can rewrite the rational function as A/(x - 2) + B/(x - 2)^2, where A and B are the unknown coefficients. By equating the numerators, we can solve for A and B and then simplify the expression as needed.