Topic Details (Notes format)

How to Solve Rational Equations (Equations with Fractions)

Subject: Mathematics

Book: Maths Mastery

Rational equations involve fractions with polynomials. Typically, you clear denominators by multiplying the entire equation by the least common denominator (LCD). For example, if 1/(x+2) = 3/(2x+4), multiply both sides by (x+2)(2x+4). Simplify, solve, and verify no denominator is zero. Rational equations arise in rate problems, mixture questions, or advanced algebra tasks. By systematically removing fraction complexities, you can isolate variables accurately, reinforcing strong algebraic fundamentals vital to real-world modeling and advanced problem-solving.

Practice Questions

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

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What is the HCF of 72 and 120?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If the perimeter of a square is 40 cm, what is the area of the square?

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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 sum of all angles in a hexagon?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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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 a+b = 10 and ab = 21, what is the value of (a-b)^2?

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

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