Скачать или смотреть Solving fraction equations with algebra

*CORE CONCEPT*
Solving fraction equations involves manipulating algebraic expressions with fractions to isolate variables. This process requires understanding how to eliminate denominators and apply algebraic rules.

*TOPICS COVERED*
When to use multiplication to eliminate denominators in fractional equations (B1)
How to simplify fractional equations step by step (B1)
When to apply standard algebraic operations to solve for variables (B1)

*EXAMPLE SENTENCES*
Example 1: If 1/x = 1/2, multiply both sides by x → 1 = x/2. Then multiply both sides by 2 → x = 2.
Example 2: If 3/(x + 1) = 1/4, multiply both sides by (x + 1) → 3 = (x + 1)/4. Then multiply both sides by 4 → 12 = x + 1 → x = 11.
Example 3: If 2/(x - 3) = 3/5, multiply both sides by (x - 3) → 2 = 3(x - 3)/5. Then multiply both sides by 5 → 10 = 3(x - 3). Expand → 10 = 3x - 9 → 3x = 19 → x = 19/3.

*GRAMMAR RULES*
Write the fractional equation → multiply both sides by the same number to eliminate denominators.
Use multiplication → clear the fraction and simplify the equation.
Solve for the variable → apply standard algebraic operations.

*COMMON ERRORS*
Wrong: Writing x = 2 immediately for 1/x = 1/2 → Right: Multiply both sides by the same number to maintain equality.
Wrong: Multiplying both sides by different values → Right: Eliminate denominators before solving for the variable.
Wrong: Ignoring the fraction part when solving for x → Right: Simplify the resulting algebraic equation correctly.

*STUDENT QUESTIONS*
How do I solve a fraction equation?
When should I eliminate denominators in algebra?
Is my solution for x correct in this example?
What's the difference between multiplying both sides by the same number and different numbers?

*KEY CONCEPTS*
Fraction equations, algebraic expressions, solving for variables, B1 level, algebra rules.