You must complete Logarithms 3 to unlock this Lesson.

ALGEBRAIC FRACTIONS

CONTENT

  1. Simplification of fractions.
  2. Operations in algebraic fractions.
  3. Equations involving fractions.
  4. Substitution in fractions.
  5. Simultaneous equations involving fractions.
  6. Undefined value of a fraction.

SIMPLIFICATION OF FRACTIONS

An algebraic fraction is a part of a whole, represented mathematically by a pair of algebraic terms. The upper part is called the numerator while the lower part the denominator. To simplify algebraic fractions, we need to factorize both the numerator and the denominator.

Examples:

1. Reduce the following to their lowest terms

(a) \(\frac{3x^2 + 9x^2 y^2}{3x^2 y}\)

(b) \(\frac{x^2 -y^2 + 3x + 3y}{x -y + 3}\)

(c) \(\frac{x^2 -9}{x^2 + x -6}\)

(d) \(\frac{5xy -10x+y -2}{8 -2y^2}\)

Solution:

(a) \(\frac{3x^2 + 9x^2 y^2}{3x^2 y}\) \( =\frac{3x^2 (1 + 3y^2)}{3x^2 × y}\)

Cancel the common factors i.e. \( 3x^2\)

∴ Answer \( = \frac{1 + 3y^2}{y}\)

(b) \(\frac{x^2 -y^2 + 3x + 3y}{x -y + 3}\) \(= \frac{(x + y)(x -y) + 3(x + y)}{x -y + 3} \\ = \frac{(x + y)(x -y + 3)}{x -y +3} \)

∴ Ans \(= x + y\)

(c) \(\frac{x^2 -9}{x^2 + x -6}\) \(= \frac{(x + 3)(x -3)}{(x + 3)(x -2)} \\ = \frac{x -3}{x -2}\)

(d) \(\frac{5xy -10x+y -2}{8 -2y^2}\) \(= \frac{5x(y -2) + (y -2)}{2(4 -y^2)} \\ = \frac{(y -2)(5x + 1)}{2(2 -y)(2 + y)} \\ = \frac{-(2 -y)(5x + 1)}{2(2 -y)(2 + y)} \\= \frac{-(5x + 1)}{2(2 + y)} \)

Class Activity:

Simplify the following fractions

1.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS2 General Mathematics, SS2 General Mathematics Evaluation Questions, SS2 General Mathematics Evaluation Questions Second Term, SS2 General Mathematics Objective Questions, SS2 General Mathematics Objective Questions Second Term, SS2 General Mathematics Second Term
Back to: GENERAL MATHEMATICS – SS2 > Second Term
© [2022] Spidaworks Digital - All rights reserved.
error: Alert: Content is protected !!