Maths-

General

Easy

Question

# The partial fractions of are

Hint:

### The partial fraction decomposition is writing a rational expression as the sum of two or more partial fractions. The following steps are helpful to understand the process to decompose a fraction into partial fractions.

**Step-1:** Factorize the numerator and denominator and simplify the rational expression, before doing partial fraction decomposition.
**Step-2:** Split the rational expression as per the formula for partial fractions. P/((ax + b)^{2} = [A/(ax + b)] + [B/(ax + b)^{2}]. There are different partial fractions formulas based on the numerator and denominator expression.
**Step-3:** Take the LCM of the factors of the denominators of the partial fractions, and multiply both sides of the equation with this LCM.
**Step-4:** Simplify and obtain the values of A and B by comparing coefficients of like terms on both sides.
**Step-5:** Substitute the values of the constants A and B on the right side of the equation to obtain the partial fraction.

**Step-1:**Factorize the numerator and denominator and simplify the rational expression, before doing partial fraction decomposition.**Step-2:**Split the rational expression as per the formula for partial fractions. P/((ax + b)^{2}= [A/(ax + b)] + [B/(ax + b)^{2}]. There are different partial fractions formulas based on the numerator and denominator expression.**Step-3:**Take the LCM of the factors of the denominators of the partial fractions, and multiply both sides of the equation with this LCM.**Step-4:**Simplify and obtain the values of A and B by comparing coefficients of like terms on both sides.**Step-5:**Substitute the values of the constants A and B on the right side of the equation to obtain the partial fraction.## The correct answer is:

### Given :

Step-1: Split the rational expression as per the formula for partial fractions.

Step-2: Take the LCM of the factors of the denominators of the partial fractions, and multiply both sides of the equation with this LCM.

.

Step-3: Simplify and obtain the values of A , B , C and D by comparing coefficients of like terms on both sides

Step-4: Substitute the values of the constants A, B , C and D on the right side of the equation to obtain the partial fraction.

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