plz i cerious need help i posted dis qustion bt due 2 my wrong typing it was nt anser plz here it is:x^4+3x-2/(x^2+1)=Ax+B/(x^2+1)+Cx+D/(x^2+1)^2+(Ex+F)/(x^2+1)^3+G/(x-4)+(Hx+1)/(x-4)^2.find ABCDEFGH? plz it a partial fraction thank yo u and Godbless u

You appear to want

x^4+3x-2
--------------------------
(x^2+1)^3 (x-4)^2

You manage to mangle things badly, and the solution to that fraction has been posted in response to an earlier version of the poorly typed question. Here it is again.

http://www.wolframalpha.com/input/?i=%28x^4%2B3x-2%29%2F%28%28x^2%2B1%29^3+%28x-4%29^2%29

just scroll down a bit to see the partial fraction expression.

AND STOP POSTING MISTYPED PROBLEMS!

To find the values of ABCDEFGH in the given partial fraction expression, we can follow these steps:

Step 1: Multiply the entire equation by the denominator (x^2 + 1)(x - 4)(x - 4)^2(x^2 + 1)^3 to eliminate the fractions.

(x^4 + 3x - 2) [ (x^2 + 1)(x - 4)(x - 4)^2(x^2 + 1)^3 ] = A(x - 4)(x - 4)^2(x^2 + 1)^3 + B(x^2 + 1)(x - 4)(x - 4)^2(x^2 + 1)^2 + Cx(x - 4)(x - 4)^2(x^2 + 1)^2 + D(x^2 + 1)^2(x - 4)(x - 4)^2(x^2 + 1) + E(x^2 + 1)^3(x - 4)(x - 4)^2 + F(x^2 + 1)^3(x - 4) + G(x^2 + 1)(x - 4)^2(x^2 + 1)^3 + Hx(x^2 + 1)(x - 4)(x^2 + 1)^3 + (x^2 + 1)(x - 4)(x^2 + 1)^3.

Step 2: Simplify the equation by expanding and collecting like terms.

x^4 + 3x - 2 = A(x^6 - 8x^5 + 23x^4 - 16x^3 + 21x^2 - 80x + 80) + B(x^5 - 4x^3 + 4x) + C(x^5 - 4x^3 + 4x) + D(x^4 - 8x^2 + 16)(x^2 + 1) + E(x^4 - 8x^2 + 16) + F(x^4 - 8x^2 + 16) + G(x^6 - 8x^5 + 23x^4 - 16x^3 + 21x^2 - 80x + 80) + Hx(x^6 - 8x^5 + 23x^4 - 16x^3 + 21x^2 - 80x + 80) + (x^6 - 8x^5 + 23x^4 - 16x^3 + 21x^2 - 80x + 80).

Step 3: Simplify further by grouping and rearranging terms.

x^4 + 3x - 2 = (A + G + Hx + 1) x^6 + (-8A - 8G - 8H) x^5 + (23A + B + C - 8G - 8H) x^4 + (-16A - 16B - 16C + D + E + F + 21H) x^3 + (21A + 16D - 16E - 16F - 80H) x^2 + (-80A + 4B + 4C + 80D + 80E + 80F - 80G) x + (80A).

Step 4: Compare like terms on both sides of the equation to determine the values of ABCDEFGH.

From the equality of the coefficients of each power of x, we can extract the following relationships:

Coefficient of x^6: A + G + H = 0
Coefficient of x^5: -8A - 8G - 8H = 0
Coefficient of x^4: 23A + B + C - 8G - 8H = 1
Coefficient of x^3: -16A - 16B - 16C + D + E + F + 21H = 0
Coefficient of x^2: 21A + 16D - 16E - 16F - 80H = 0
Coefficient of x: -80A + 4B + 4C + 80D + 80E + 80F - 80G = 3
Constant term: 80A = -2

We have obtained a system of equations for the variables A, B, C, D, E, F, G, and H. Solve this system simultaneously to find the values of each variable.