Question

Multiply and find the domain. x^2-1/5xy * x^2y/1+x

I already know what the answer is (x^2-x/5) but dont know how to find the domain

Answer 1

The domain is all real numbers: (-∞, ∞).

Explanation:

Given expression:

`(x^2-1)/(5xy) \cdot ( x^2y)/(1+x)`

`\textsf{Apply the fraction rule:} \quad (a)/(b)\cdot(c)/(d)=(ac)/(bd)`

`\implies ((x^2-1)x^2y)/(5xy(1+x))`

Rewrite (x² - 1) as (x + 1)(x - 1):

`\implies (x^2y(x+1)(x-1))/(5xy(1+x))`

Cancel the common factor xy(x + 1):

`\implies (x(x-1))/(5)`

Simplify:

`\implies (x^2-x)/(5)`

The domain of the expression is unrestricted since the denominator is an integer rather than an expression. Therefore, the domain is all real numbers:

• Solution: -∞ < x < ∞
• Interval notation: (-∞, ∞)