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

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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What is the HCF of 48 and 180?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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What is the remainder when 5^100 is divided by 3?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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What is the sum of all even numbers between 1 and 50?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the square root of 144?

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