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

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If a = 4 and b = 5, what is the value of (a+b)^2?

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

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If x^2 - 6x + 9 = 0, what is the value of x?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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

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