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

What is the sum of all even numbers between 1 and 50?

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What is the area of a circle with a diameter of 14 cm?

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

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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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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If 2x = 16, what is the value of x?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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What is the HCF of 48 and 180?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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