Question

Decompose

4x2-14x + 2 devided by 4x2-1

into partial fractions (show all the steps).

Answer 1

You may factor the bottom first.

Answer 2

It is a difference of two squares.\[a ^{2}-b ^{2}=(a-b)(a+b)\]

Answer 3

yeah i get that, im confused about the top. do i assign letters as it is or do i have to simplify?

Answer 4

you will assign letters first.

Answer 5

okay thanx.

Answer 6

welcome. :)

Answer 7

what method should i use to find A and B? after i have multiplied out.

Answer 8

you mean, you already multiplied the lcd lcd on both sides? let me see your work for clarity. :))

Answer 9

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

Answer 10

that is correct so far.

Answer 11

thanx, whtas my next step?
im a lil confused by the power on the LHS i guess.

Answer 12

The polynomial on the left of the equal sign must have the same coefficients as the polynomial on the right of the equal sign.

Answer 13

okay,do i check that as the eqn stands oh do i have to multiply out? and if i do mutliply out will we be counting A and b as coefficients?

Answer 14

i have 3 coefficients on the lhs and im wondering about the rhs?

Answer 15

we can equate the coefficients of "x" first.

Answer 16

the roots rights? oh i think i get it now.

Answer 17

thanx

Answer 18

welcome again. :)