Question

Review the work showing the first few steps in writing a partial fraction decomposition.

12x–25/4x²-12x+9 = A/2x-3 + B/(2x-3)²
12x-25 = A(2x-3)+B
12x-25 = 2Ax-3A+B

what is the partial fraction decomposition in terms of x?
a. 6/2x-3 + 43/(2x-3)²
b. 6/2x-3 - 43/(2x-3)²
c. 6/2x-3 + 7/(2x-3)²
d. 6/2x-3 - 7/(2x-3)²

Answer 1

After partial fraction decomposition, the correct expression we get is,

(12x - 25)/(4x² - 12 x + 9) = (6)/(2x-3) - (7)/((2x-3)²) and the correct option is D.

Partial fractions is a technique used in mathematics to decompose a rational function into simpler fractions.

It involves breaking down a rational function with a denominator of a higher degree into a sum of fractions with simpler denominators.

The given expression is,

(12x - 25)/(4x² - 12 x + 9) = (A)/(2x-3) + (B)/((2x-3)²)

(12x - 25)/(4x² - 12 x + 9) = (A(2x-3) + B)/(4x² - 12 x + 9)

[since (a-b) = a² + b² -2ab]

Simplifying we get

12x - 25 = A(2x - 3) + B

12x - 25 = 2Ax + (B - 3A)

Comparing the coefficients we get

2A = 12

A = 6 and B - 3A = -25

Put the value of A we get

B = -7

Hence, After substituting the values of A and B in the given expression we get (12x - 25)/(4x² - 12 x + 9) = (6)/(2x-3) - (7)/((2x-3)²) and the correct option is D.