Algebraic expressions - simplifying

In summary, the conversation involves someone seeking help with algebra problems while studying for the GRE. They are struggling with simplifying a complex equation and are hoping for guidance. The advice given is to write the equation with a common denominator and not to be afraid of the size of the resulting answer.
  • #1
Rationalist
4
0
Hi all,

I'm retaking the GRE soon and I keep making stupid algebra mistakes in my calculus problems so I'm going through a textbook from 1965 that is helpful but has me stumped on some problems. I hope someone can steer me in the right direction.

1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c)

Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. Thanks in advance
 
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  • #2
It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
 
  • #3
Write everything with a denominator of (a-b)(a-c)(b-c) and add the fractions.
 
  • #4
basic advice: do not fear to write something down, just because you think it will be large and unmanageable. you have to plunge in without fear of what will come out. you have to get your hands dirty.
 

Related to Algebraic expressions - simplifying

1. What is an algebraic expression?

An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Examples include 4x + 3, 2a^2 + 5b, and 3xy - 2.

2. What does it mean to simplify an algebraic expression?

Simplifying an algebraic expression means to reduce the expression to its simplest form by combining like terms and using the rules of operations. This is done to make the expression easier to work with and to find its value for different values of the variables.

3. How do you simplify an algebraic expression?

To simplify an algebraic expression, you must first combine like terms by adding or subtracting them. Then, use the distributive property to remove parentheses and combine any remaining like terms. Finally, use the rules of exponents to simplify any terms with exponents.

4. Why is it important to simplify algebraic expressions?

Simplifying algebraic expressions is important because it allows us to easily solve equations and evaluate expressions. It also helps us to see the relationships between different terms in the expression and to identify patterns.

5. Can you provide an example of simplifying an algebraic expression?

Yes, for example, let's simplify the expression 2x + 3x + 5 - 2x. First, we combine like terms: 2x + 3x - 2x = 3x. Then, we combine the constant terms: 3x + 5. This is the simplified form of the original expression.

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