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.