Fanfiction
Rational Expressions: Simplifying
Thinking back to when you were dealing with whole-number fractions, one of the first things you did was simplify them: You "cancelled off" factors which were in common between the numerator and denominator. You could do this because dividing any number by itself gives you just "1", and you can ignore factors of "1". ADVERTISEMENT Using the same reasoning and methods, let's simplify some rational expressions.
• Simplify the following expression: To simplify a numerical fraction, I would cancel off any common numerical factors. For this rational expression (this polynomial fraction), I can similarly cancel off any common numerical or variable factors.
The numerator factors as (2)(x); the denominator factors as (x)(x). Anything divided by itself is just "1", so I can cross out any factors common to both the numerator and the denominator. Considering the factors in this particular fraction, I get:
Then the simplified form of the expression is:
Reflection:
- I think about this lesson; I find it quite hard to understand, as most math problems are. But that would be merely because of my difficulty in math. I would be honest, math doesn’t easily enter my brain and when it does; it comes off as easy as it got in… Kinda’ weird. But it’s true.
Adding and Subtracting Rational Expressions: Introduction (page 1 of 3)
Addition and subtraction are the hardest things you'll be doing with rational expressions because, just like with regular fractions, you'll have to convert to common denominators. Everything you hated about adding fractions, you're going to hate worse with rational expressions. But stick with me; you can get through this!
Let's refresh by looking at an example with regular fractions:
• Simplify the following: To find the common denominator, I first need to find the least common multiple (LCM) of the three denominators. (For old folks like me, whenever you see "LCM",
Thinking back to when you were dealing with whole-number fractions, one of the first things you did was simplify them: You "cancelled off" factors which were in common between the numerator and denominator. You could do this because dividing any number by itself gives you just "1", and you can ignore factors of "1". ADVERTISEMENT Using the same reasoning and methods, let's simplify some rational expressions.
• Simplify the following expression: To simplify a numerical fraction, I would cancel off any common numerical factors. For this rational expression (this polynomial fraction), I can similarly cancel off any common numerical or variable factors.
The numerator factors as (2)(x); the denominator factors as (x)(x). Anything divided by itself is just "1", so I can cross out any factors common to both the numerator and the denominator. Considering the factors in this particular fraction, I get:
Then the simplified form of the expression is:
Reflection:
- I think about this lesson; I find it quite hard to understand, as most math problems are. But that would be merely because of my difficulty in math. I would be honest, math doesn’t easily enter my brain and when it does; it comes off as easy as it got in… Kinda’ weird. But it’s true.
Adding and Subtracting Rational Expressions: Introduction (page 1 of 3)
Addition and subtraction are the hardest things you'll be doing with rational expressions because, just like with regular fractions, you'll have to convert to common denominators. Everything you hated about adding fractions, you're going to hate worse with rational expressions. But stick with me; you can get through this!
Let's refresh by looking at an example with regular fractions:
• Simplify the following: To find the common denominator, I first need to find the least common multiple (LCM) of the three denominators. (For old folks like me, whenever you see "LCM",