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 value of log₃(27)?

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What is the LCM of 15 and 20?

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If 8x = 512, what is the value of x?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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What is the sum of the first 10 positive even numbers?

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What is the sum of the first 20 odd numbers?

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

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

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A cube has a side length of 4 cm. What is its volume?

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