2·t3 + 11·t2 − 7·7 − 6
(3·a4 − 2·a3 + 7·a2 − 1)·(2·a3 + 3·a2 − 1)
6·a7 + 5·a6 + 8·a5 + 18·a4 − 10·a2 + 1
(3·a4 − 2·a3 + 7·a2 − 1) / (2·a3 + 3·a2 − 1)
quotient and remainder of (3*a^4-2*a^3+7*a^2-1) / (2*a^3+3*a^2-1)
WolframAlpha
quotient: (3*a)/2 - 13/4 remainder: 67*a^2/4 + 3*a/2 - 17/4
Another example:
(1/3*x^3 + 5/13*x^2 - 1) * (2/7*x^2 + 3) → 2/21*x^5 + 10/91*x^4 + x^3 + 79/91*x^2 - 3
one way (using script-calculator and then script-fractions):
1 / 3 = 0.3333333333333333 5 / 13 = 0.38461538461538464 2 / 7 = 0.2857142857142857
0.09523809523809523*x^5 + 0.10989010989010989*x^4 + 1*x^3 + 0.8681318681318683*x^2 - 3
then:
095238/999999 + 0/1 → 2/21
109890/999999 + 0/1 → 10/91
868131/999999 + 0/1 → 79/91
2/21*x^5 + 10/91*x^4 + x^3 + 79/91*x^2 - 3
another way (using only script-fractions):
5/13 * 2/7 → 10/91
1/3 * 2/7 → 2/21
5/13 * 3/1 → 15/13
15/13 - 2/7 → 79/91
2/21*x^5 + 10/91*x^4 + x^3 + 79/91*x^2 - 3