Algebraic fractions and binary operations

Question 1 of 10

(x + 2)/(x + 2) = 1 for all x.

Question 2 of 10

A binary operation * is commutative if

Question 3 of 10

Simplify (x² − 9)/(x − 3).

Question 4 of 10

If a * b = a + b + 4 on the real numbers, find the identity element.

Question 5 of 10

The inverse a⁻¹ of a under * satisfies

Question 6 of 10

The identity element e of * satisfies

Question 7 of 10

Under ordinary addition on the integers, the identity element is

Question 8 of 10

A binary operation * is defined on the real numbers by a * b = a + b + 4ab. (a) Show that * is commutative. (b) Find the identity element. (c) Find the inverse of 4 under *.

Question 9 of 10

If x * y = xy − x, then 4 * 4 = ___

Question 10 of 10

Ordinary subtraction is commutative.