Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

Factor the numerators/ denominators where possible

x² + 7x + 10 = (x+ 2)(x + 5)

x² - 3x - 18 = (x - 6)(x + 3)

x² + x - 2 = (x + 2)(x - 1)

Hence

= $\frac{(x+2)(x+5)}{x+3}$ × $\frac{(x-6)(x+3)}{(x+2)(x-1)}$

Cancel the factors (x + 2) and (x + 3) on numerator/denominator

= $\frac{(x+5)(x-6)}{x-1}$ ← in simplest form

The denominator of the product cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve x - 1 = 0 ⇒ x = 1 ← restricted value