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Understanding algebraic expressions and equations is crucial in mathematics. These expressions consist of numbers, variables, and operations, while equations equate two expressions. Fractions play a significant role, leading to rational expressions and equations. Solving these often involves finding a common denominator or using advanced techniques like factorizing and grouping. The text provides strategies for dealing with fractions in algebra, emphasizing the importance of maintaining balance and simplifying equations to find unknown variables.

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## Basics of Algebra

### Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and arithmetic operations

### Constants and Variables

Constants are specific numbers, while variables represent unknowns and are usually denoted by letters

### Equations

Equations are mathematical statements that two expressions are equal, indicated by an equals sign

## Fractions in Algebra

### Rational Expressions

Rational expressions are algebraic expressions that include fractions

### Rational Equations

Rational equations are equations that involve fractions

### Solving Equations with Fractions

To solve equations with fractions, one must find a common denominator and eliminate the fractions

## Techniques for Simplifying Algebraic Expressions

### Factorization

Factorization involves rearranging and grouping similar terms, then factoring out common factors

### Grouping

Grouping involves rearranging and grouping similar terms in an algebraic expression

### Simplifying Rational Expressions

To simplify rational expressions, one can use techniques such as factorization and grouping

## Solving Equations with Fractions

### Eliminating Fractions

One strategy for solving equations with fractions is to eliminate the fractions by multiplying every term by the LCD

### Isolating the Variable

The solution to an equation with fractions is obtained by isolating the variable and solving for its value

### Checking the Solution

The solution to an equation with fractions can be checked by substituting it back into the original equation to confirm equality

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