Exam Questions – Simplifying a rational expression

Exam Questions – Simplifying a rational expression

Simplifying Rational Expressions

Introduction

  • A rational expression is essentially a fraction in which the numerator and/or the denominator are algebraic expressions.
  • Such expressions can frequently be simplified or reduced to more simple forms, similar to simplifying normal fractions.

Procedure for Simplifying Rational Expressions

  • The first step is to factor the numerator and the denominator of the rational expression.
  • You can then simplify the rational expression by cancelling out common factors present in both the numerator and the denominator.
  • Keep in mind that, similar to basic fractions, simplifying a rational expression does not change its value.

Examples

  • If you have the rational expression 6x^2/3x, you can factor the numerator as 2x(3x) and the denominator as 3x(1). As 3x is a common factor, it can be cancelled out, simplifying the expression to 2x.
  • Similarly, the rational expression 15x^3 - 10x^2 / 5x^2 can be simplified by factoring the numerator to 5x^2(3x - 2) and the denominator to 5x^2(1). The common factor of 5x^2 can be cancelled out, simplifying the expression to 3x - 2.

Practical Applications

  • Simplifying rational expressions is key in solving more complex algebraic problems and equations.
  • It is also a necessary skill in various branches of mathematics beyond algebra, such as calculus and geometry.

Conclusion

  • Proficiency in simplifying rational expressions is a must for anyone studying algebra.
  • Continuous practice is the best way to master this skill.
  • Remember to always factorise the numerator and denominator first, before proceeding with the simplification process.