Topic Details (Notes format)

How to Reduce Algebraic Fractions with Polynomials

Subject: Mathematics

Book: Maths Mastery

To reduce or simplify algebraic fractions, factor both numerator and denominator completely, then cancel common factors, ensuring they are non-zero in the original domain. For example, (x²–1)/(x²–x–2) factors to (x–1)(x+1)/(x–2)(x+1). Cancel (x+1) for x≠–1, leaving (x–1)/(x–2). This process is identical to fraction simplification but extended to polynomials. Mastery enables you to handle advanced rational expressions in calculus integrals, partial fractions, and engineering equations that combine polynomial-based denominators and numerators for streamlined analysis.

Practice Questions

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

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

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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What is the area of an equilateral triangle with side length 10 cm?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(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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If a square has a perimeter of 64 cm, what is its area?

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