Partial Fraction Decomposition

[BaseballB6236]

Find the partial fraction decomposition of

-3
---------------
4x^2-6x+2






so far I have:

-3 -3
---------------- = ----------------------
2(2x^2-3x+1) 2(2x-1)(x-1)




= A/2 + B/ 2x-1 + C/x-1


= A(2x-1)(x-1) B(2)(x-1) C(2)(2x-1)
------------------------- + ---------------------- + --------------------
2(2x-1)(x-1) 2(2x-1)(x-1) 2(2x-1)(x-1)


on the right track? what should I do next..thanks in advance

 

[BigGlenntheHeavy]

\(\displaystyle BaseballB6236, \ once \ you \ get \ the \ pattern \ down \ (grunt \ work), \ then \ if \ you \ have \ a\)

\(\displaystyle trusty \ TI-89, \ go \ to \ (on \ the \ Home \ menu) \ F2-3 \ (expand) \ and \ plugged \ in\)

\(\displaystyle expand \bigg(\frac{-3}{4x^2-6x+2},x\bigg) \ and \ you \ will \ get, \ to \ wit:\)

\(\displaystyle \frac{3}{2x-1}-\frac{3}{2(x-1)}, \ thereby \ avoiding \ all \ the \ grunt \ work.\)

 

[BaseballB6236]

thanks