Operations with Rational Numbers - Grade 12
This worksheet focuses on advanced operations with rational numbers, including addition, subtraction, multiplication, and division, suitable for Grade 12 students.
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Operations with Rational Numbers
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Carefully read each question and perform the indicated operations with rational numbers. Simplify all answers to their lowest terms.
1. Simplify the following expression: (2x / (x^2 - 4)) + (3 / (x + 2))
2. Subtract: (5 / (x^2 - 9)) - (1 / (x - 3))
3. Multiply: ((x^2 - 16) / (x^2 - 4x)) * ((x^2) / (x^2 + 8x + 16))
4. Divide: ((x^2 - 25) / (x^2 - 4x - 5)) / ((x^2 + 5x) / (x + 1))
5. Which of the following is equivalent to (1 / x) + (1 / y)?
(x + y) / xy
2 / (x + y)
1 / (x + y)
xy / (x + y)
6. What is the product of (x / (x + 1)) and ((x + 1) / (x - 1))?
x / (x - 1)
(x + 1) / (x - 1)
x
1 / (x - 1)
7. When adding or subtracting rational expressions, you must first find a .
8. To divide rational expressions, you multiply the first expression by the of the second expression.
9. The expression (x + 3) / (x^2 - 9) can be simplified to 1 / (x - 3).
True
False
10. The product of two rational expressions is always a rational expression.
True
False