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 cube root of 729?

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The probability of rolling a sum of 7 with two dice is:

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What is the HCF of 48 and 180?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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What is the square root of 121?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If the radius of a circle is doubled, what happens to its area?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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If the radius of a circle is 7 cm, what is its circumference?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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