Partial Fractions - [Pure 3].

Question 1

How do you simplify Algebraic Fractions?

Answer 1

Factorise into their brackets and then cancel the brackets where necessary.

Question 2

How do you solve Partial Fractions?

Answer 2

1. Set the numerator of the fraction to simplify equal to the cross product numerator with the unknown variables. [e.g. (3x+1) = A(x-2) + B(2x)].
2. Sub in values for x which will make the brackets equal to zero. This will cancel out brackets and leave you to finding the unknowns.
3. Replace the letters with the values found.

Question 3

What is the general form of a partial fraction which splits into 3 fractions?

Answer 3

px+q / (ax+b)(cx+d)(ex+f) ≡ [A / (ax+b)] + [B / (cx+d)] + [C / (ex+f)].

Question 4

What is the general form of a partial fraction which splits into 3 fractions where one is a square denominator?

Answer 4

px+q / (ax+b)(cx+d)² ≡ [A / (ax+b)] + [B / (cx+d)] + [C / (cx+d)²].

Question 5

How do you solve partial fractions with a squared bracket on the denominator?

Answer 5

1. Set the numerator of the fraction to simplify equal to the cross product numerator with the unknown variables. [e.g. (5x+3) / (2x+1)(x+1)² –> 5x+3 = A / (x+1) + B / (x+1)² + C / (2x+1) –> A(x+1)(2x+1) + B(2x+1) + C (x+1)²].