I'll do one, and you can do the other. You can check your work at wolframalpha.com
x^3-x = x(x-1)(x+1) so we want
A/x + B/(x-1) + C/(x+1) = (3x^2-7x-2)/(x^3-x)
So, using the common denominator, we have
A(x^2-1) + Bx(x+1) + Cx(x-1) = 3x^2-7x-2
(A+B+C)x^2 + (B-C)x - A = 3x^2-7x-2
If they are identical, then
A+B+C = 3
B-C = -7
-A = -2
So,
A = 2
B = -3
C = 4
and we have
2/x - 3/(x-1) + 4/(x+1)
check at
http://www.wolframalpha.com/input/?i=partial+fractions+%283x^2-7x-2%29%2F%28x^3-x%29
Write out the partial fraction decomposition of the following rational expression.
1.) 3x^2-7x-2/x^3-x
2.) x^3-x+3/x^2+x-2
1 answer
1 answer