Скачать или смотреть Partial Fraction method by mronkoshorts 🔥💯 |Partial fractions jee mains | Maths class 12 🎯

Partial Fraction method by mronkoshorts 🔥💯 |Partial fractions jee mains | Maths class 12 🎯
How to solve Partial Fractions..let's learn with partha sir

Partial fractions are a technique used in algebra to break down a complex rational expression (a fraction where both the numerator and denominator are polynomials) into a sum of simpler fractions. This is often helpful for integration and other mathematical operations.
The Basic Idea
Imagine you have a fraction like:

The goal of partial fraction decomposition is to express this as a sum of simpler fractions, like:
where the denominators of the simpler fractions are factors of the original denominator.
Types of Factors and Their Corresponding Partial Fractions
Linear Factors:
If the denominator has a linear factor (like (x - a)), the corresponding partial fraction will be of the form:

Repeated Linear Factors:
If the denominator has a repeated linear factor (like (x - a)^n), the partial fractions will be of the form:

Quadratic Factors:
If the denominator has an irreducible quadratic factor (like (ax^2 + bx + c)), the corresponding partial fraction will be of the form:

Repeated Quadratic Factors:
If the denominator has a repeated irreducible quadratic factor (like (ax^2 + bx + c)^n), the partial fractions will be of the form:

Steps to Find Partial Fractions
Factor the Denominator: Factor the denominator of the original rational expression into linear and/or quadratic factors.
Set Up the Partial Fractions: Write the original expression as a sum of partial fractions, using the appropriate forms based on the factors of the denominator.
Find the Unknown Coefficients: Multiply both sides of the equation by the original denominator to clear the fractions. Then, equate coefficients of like terms on both sides to solve for the unknown coefficients in the partial fractions

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