Question

Consider the rational expression (IMAGE ATTACHED)

3x^2−3/
3x^2+2x−1

Which statements are true?

Answer 1

• 3x² is a term in the numerator
• x + 1 is a common factor
• The denominator has 3 terms

Explanation:

You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.

When you factor the expression, you get ...

`(3x^2-3)/(3x^2+2x-1)=(3(x^2-1))/((3x-1)(x+1))=(3(x-1)(x+1))/((3x-1)(x+1))`

This reveals a common factor of x+1.

So, the above three observations are true of this rational expression.