What is the quotient in simplest form? State any restrictions on the variable.

Question

x^2-4/z-3 / z+2/x^2+z-12

Answer 1

To simplify the given quotient we need to factor the numerator and denominator:

x^2 - 4 = (x + 2)(x - 2)
x^2 + z - 12 = (x + 4)(x - 3)

Therefore, the given expression becomes:

((x + 2)(x - 2)) / (z - 3) * ((x - 3)(z + 2) / (x + 4)(x - 3))

We can cancel out the common terms in numerator and denominator:

= (x + 2) / (x + 4)

Therefore, the answer in simplest form is (x + 2) / (x + 4). The restrictions on the variables are that x cannot be equal to -4 since that would make the denominator 0, leading to division by zero which is undefined.