(-12a^3b^5)/(4a^2b^7) state any restrictions on the variable(s) if they exist.

PLEASE HELP (30 points)

Step-by-step explanation:

So we have the rational expression:

In rational expressions, the restrictions of the expression would be the zeros of the denominator Therefore, set the denominator equal to zero and solve for its zeros:

Zero Product Property:

Solve for a and b:

Therefore, the restrictions on the variables are that a and b cannot equal zero.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0