Homework SourseCan someone show me how to do long division of x7 1x 1 On
Can someone show me how to do long division of \"x^7 - 1/x - 1 ?\" (On scratch paper if you can)
....
The answer is x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
----
Please show me how to do this? I\'ve been trying, and can\'t come up with the correct answer?
Again, please on paper, and not typed out. :)
....
The answer is x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
----
Please show me how to do this? I\'ve been trying, and can\'t come up with the correct answer?
Again, please on paper, and not typed out. :)
Solution
Perform long division, then do a partial fraction decomposition. (x² - 5x + 1)/(x² + x) = 1 + (-6x + 1)/(x(x + 1)). Put (-6x + 1)/(x(x + 1)) = A/x + B/(x + 1) ==> -6x + 1 = A(x + 1) + Bx = (A + B)x + A. Comparing coefficients of x and the constant, A = 1 and A + B = -6 ==> B = -7. So ? (x² - 5x + 1)dx/(x² + x) = ? 1 + 1/x - 7/(x + 1) dx = x + ln|x| - 7ln|x + 1| + C.![Can someone show me how to do long division of \](/WebImages/46/can-someone-show-me-how-to-do-long-division-of-x7-1x-1-on-1146971-1761616690-0.webp "Can someone show me how to do long division of \")
