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Algebraic Fractions Review
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Algebraic Fractions Review
📚 Part 1: Simplifying and Basic Operations
1. Simplify the following algebraic fraction:
6x²/9x = ___________
2. Which of these is equivalent to (2x + 4)/2?
x + 2
x + 4
2x + 2
x + 8
3. Multiply: (3/x) × (x²/6) =
4. Add the fractions: 2/x + 3/x =
Answer: ___________
5. Factorise the numerator and denominator, then simplify:
(x² - 4)/(x + 2) =
✏️ Part 2: Operations with Unlike Denominators
6. Add: 1/x + 2/(3x)
Show your working to find a common denominator:
Final answer: ___________
7. Subtract: 5/(2x) - 1/(4x) =
8. Which step is the first step when adding algebraic fractions with different denominators?
Add the numerators
Find the lowest common denominator
Factorise the numerators
Cross multiply
🎯 Part 3: Problem Solving
9. A formula for calculating efficiency is E = (P₁ + P₂)/(2T), where P₁ and P₂ are power outputs and T is time. If P₁ = 3x, P₂ = x, and T = 2x, write the simplified expression for E.
E = ___________
10. Solve for x: 3/x = 6/8
x = ___________
11. Explain in your own words why we need to factorise when simplifying algebraic fractions:
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