When simplifying a rational fraction, why do you need to factor the numerator and the denominator? Include two examples!

I will be happy to critique your thinking on this.

I wouldn't ask if I knew how to guess

Ms. Sue Ms. Sue answered
8 years ago

That's the dumbest thing I've ever heard.

Edward Edward answered
7 years ago

because they're equilevant then

meh meh answered
6 years ago

Don't be so rude Ms.Sue!!!

Frank Frank answered
5 years ago

This is the second question of jiskha

Fire Star Fire Star answered
4 years ago

THE 2nd QUESTION!!

IMSOCooL IMSOCooL answered
3 years ago

The second Q

Explain Bot Explain Bot answered
7 months ago

I apologize for any misunderstanding. When simplifying a rational fraction, factoring the numerator and denominator helps us find common factors that can be crossed out, which simplifies the expression further. This process is similar to canceling out common terms in algebraic equations.

Let's look at two examples to illustrate this:

Example 1:
Simplify the fraction 12/18.

Step 1: Factor the numerator and denominator:
12 = 2 × 2 × 3
18 = 2 × 3 × 3

Step 2: Cancel out common factors:
12/18 = (2 × 2 × 3)/(2 × 3 × 3) = (2/2) × (2/3) × (3/3) = 1 × 2/3 × 1 = 2/3

So, 12/18 simplifies to 2/3.

Example 2:
Simplify the fraction (x^2 - 4)/(x^2 - 9).

Step 1: Factor the numerator and denominator:
x^2 - 4 = (x - 2)(x + 2)
x^2 - 9 = (x - 3)(x + 3)

Step 2: Cancel out common factors:
(x^2 - 4)/(x^2 - 9) = (x - 2)(x + 2)/(x - 3)(x + 3)

In this example, no further simplification is possible because there are no common factors left to cancel out.

Therefore, factoring the numerator and denominator helps us simplify rational fractions by identifying and removing common factors, which results in a simplified expression.

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