How Do You Simplify Complex Algebraic Expressions?

In summary, the conversation is about simplifying the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x). The attempt at a solution involved finding a common factor and adding them, but it became complicated. The expert suggests using the rule x^a/x^b=x^(a-b) and fully parenthesizing expressions. The simplified answer is x(1-x)^(1-x).
  • #1
beaf123
41
0

Homework Statement


I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x)

I want to simplify this expression.

Homework Equations


None

The Attempt at a Solution



I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it got really ugly so I think I did something wrong. Anyone knows how to simplify this one?[/B]
 
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  • #2
beaf123 said:

Homework Statement


I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x)

I want to simplify this expression.

Homework Equations


None

The Attempt at a Solution



I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it got really ugly so I think I did something wrong. Anyone knows how to simplify this one?[/B]

x^a/x^b=x^(a-b). In your case a=2/(1-x) and b=2x/(1-x). Concentrate on simplifying a-b. BTW notice I wrote 2/(1-x) instead of 2/1-x which would be interpreted as (2/1)-x. That's not what I think you mean. Always fully parenthesize expressions!
 
Last edited:
  • #3
Thanks a lot.

Very smootely my answer becomes x(1-x)
 

Related to How Do You Simplify Complex Algebraic Expressions?

1. What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains numbers, variables, and mathematical operations, but does not have an equal sign. It can be simplified or evaluated by substituting values for the variables.

2. What is the difference between an algebraic expression and an equation?

An algebraic expression does not have an equal sign, while an equation does. An equation also represents a balance or relationship between two expressions, while an algebraic expression is simply a combination of numbers, variables, and operations.

3. How do you simplify an algebraic expression?

To simplify an algebraic expression, combine like terms by adding or subtracting coefficients and keeping the variable the same. You can also use the distributive property to remove parentheses and combine like terms. Finally, you can substitute values for the variables and evaluate the expression.

4. How do you solve an algebraic expression?

To solve an algebraic expression, you need an equation with an equal sign. You can then use the properties of equality and inverse operations to isolate the variable and find its value. A solution to an algebraic expression is a value that makes the equation true when substituted for the variable.

5. What are some real-life applications of algebraic expressions?

Algebraic expressions are used in a variety of real-life situations, such as calculating the cost of a purchase with tax, determining the area of a room, and predicting the growth of a population. They are also used in more complex fields such as physics, engineering, and economics to model and solve real-world problems.

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