Topic Details (Notes format)

How to Add and Subtract Rational Expressions

Subject: Mathematics

Book: Maths Mastery

Adding and subtracting rational expressions parallels fraction operations: find a common denominator, combine numerators, and simplify. For instance, (x/(x + 2)) – (3/(x – 4)) requires an LCM of (x + 2)(x – 4). The resulting expression might then factor or simplify further. Keeping track of restricted values (where denominators are zero) is essential. This skill is key in advanced algebra, engineering formulas, or any scenario mixing polynomial-based rates. Building fluency ensures complex expressions don’t overwhelm you, allowing deeper exploration of functional relationships.

Practice Questions

What is the sum of the first 50 positive integers?

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What is the value of log₃(27)?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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What is the greatest common divisor (GCD) of 36 and 48?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If 3x = 81, what is the value of x?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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The probability of getting an even number when rolling a die is:

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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