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

If a:b = 5:7 and b:c = 6:11, what is a:c?

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If 2x - 3 = 7, what is the value of x?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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What is the sum of the first 20 odd numbers?

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What is the square root of 0.25?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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What is the length of the diagonal of a square with a side length of 7 cm?

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