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

If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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What is the HCF of 48 and 180?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If 5x - 2 = 13, what is the value of x?

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

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What is the square root of 144?

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If x - y = 5 and x + y = 15, what is the value of x?

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

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