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 angles in a hexagon?

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

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What is the square root of 144?

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

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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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 = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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If two complementary angles differ by 30°, what are the angles?

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