Topic Details (Notes format)

How to Simplify Rational Expressions

Subject: Mathematics

Book: Maths Mastery

Rational expressions are fractions with polynomials in numerator and denominator, like (x² – 9)/(x² – x – 6). Simplify by factoring both numerator and denominator, then canceling common factors. In this example, x² – 9 factors to (x – 3)(x + 3), and x² – x – 6 factors to (x – 3)(x + 2), simplifying to (x + 3)/(x + 2) if x ≠ 3. Rational expression simplification appears in advanced algebra, calculus, and real-life modeling of rates or proportions. Mastery of factoring and cautious domain considerations ensures robust, accurate algebraic manipulation.

Practice Questions

What is the sum of all odd numbers from 1 to 99?

View Question

If the average of five consecutive odd numbers is 25, what is the largest number?

View Question

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

View Question

If log(100) = 2 and log(10) = 1, what is log(1000)?

View Question

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

View Question

If x² - 9x + 18 = 0, what are the roots of the equation?

View Question

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

View Question

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

View Question

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

View Question

If the sum of the squares of two consecutive positive integers is 365, what are the integers?

View Question