Decompose 4x² - 14x plus 2 divided by 4x² - 1 into partial fractions showing all steps?

Answer 1

To solve this you must first factor the denominator into (2x+1)(2x-1) and see then that there are two variable A, and B that you need to solve for when making the partials.

From this you get the equation:

(4x2 - 14x + 2)/(4x2 - 1) = A/(2x+1) + B/(2x-1)

Let's get rid of the denominator on the right:

4x2 - 14x + 2 = A(2x-1) + B(2x+1)

now we need to plug in values for x such that either A or B is canceled out. Obviously, A is canceled out at x=1/2 and B is canceled out at x=-1/2

Solving the equations when plugging in x we get:

A=-5 and B = 2, so your final answer is:

(4x2 - 14x + 2)/(4x2 - 1) = -5/(2x+1) + 2/(2x-1)