MATTW20 Group Title Partial Fractions$\int\limits_{}^{}\frac{ dx }{ x^2(x^2-16) }$ 8 months ago 8 months ago

1. MATTW20 Group Title

so far i have A/(x)+B/(x^2)+C/(x+4)+D/(x-4)

2. ECE Group Title

Yep that's right

3. MATTW20 Group Title

then i multiplied and simplified basically there's alot more to right out but i cant seem to solve for A or B

4. ECE Group Title

If you have C and D you can sub in two arbitrary x values that aren't -4 or 4 and you can build a system of equations

5. MATTW20 Group Title

but wouldn't that leave you with two things to solve for or am i misunderstanding you

6. myininaya Group Title

$\frac{1}{x^2(x^2-16)}=\frac{Ax(x+4)(x-4)+B(x+4)(x-4)+Cx^2(x+4)+Dx^2(x-4)}{x^2(x^2-16)}$ $1=x^3(A+C+D)+x^2(B+4C-4D)+x(-16A)+(-16B)$ A and B should be easiest to solve for unless I messed up somewhere

7. ECE Group Title

sub x = 4, you find C. sub x = -4, you find D. Next you can sub x = 1 and x = 2, that gives you two equations with two unknowns you can solve.

8. myininaya Group Title

So you are suppose to have $1=x^3(0)+x^2(0)+x(0)+1$ (so we can have 1=1) and you have $1=x^3(A+C+D)+x^2(B+4C-4D)+x(-16A)+(-16B)$ You have 4 equations to solve. A+C+D=0 B+4C-4D=0 -16A=0 -16B=1 These easiest two equations to solve are the last two since there is only one unknown in each.

9. MATTW20 Group Title

ok ty