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

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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A car travels 240 km in 4 hours. What is its average speed?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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A sphere has a radius of 7 cm. What is its volume?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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If two complementary angles differ by 30°, what are the angles?

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If x^2 + 4x + 4 = 0, what is the value of x?

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What is the value of x if log(x) + log(4) = log(32)?

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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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