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

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If the sum of three consecutive integers is 72, what are the integers?

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

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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How many diagonals does a pentagon have?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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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 a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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