Perform combined operations of algebraic expressions involving expansion and factorisation

Algebraic Expressions and Basic Arithmetic Operations

2.3

Algebraic Expressions and Basic Arithmetic Operations

Addition and Subtraction of Algebraic Expressions

Rules

Before adding or subtracting two algebraic fractions, check the denominators first.
If they are not the same, you need to express all fractions in terms of common denominators.

Examples

(i)

\(\dfrac{3y}{5} + \dfrac{3y}{5} = \dfrac{6y}{5}\)

(ii)

\(\begin{aligned} &\dfrac{2}{3} - \dfrac{4s}{9} \\\\&=\dfrac{2\times 3}{3\times 3} - \dfrac{4s}{9} \\\\&= \dfrac{6-4s}{9}. \end{aligned}\)

(iii)

\(\begin{aligned} &\space \dfrac{1}{2k} - \dfrac{1}{kj} \\\\&= \dfrac{1 \times j}{2k \times j} - \dfrac{1 \times 2}{kj\times 2} \\\\& = \dfrac{j-2}{2kj}. \end{aligned}\)

Multiplication and Division

Factorise expressions before division or multiplication when it is necessary.

Example

\(\begin{aligned} &\space \dfrac{m+n}{x -y} \div \dfrac{(m+n)^2}{x^2 -y^2} \\\\& = \dfrac{\cancel{m+n}}{\cancel{x-y}} \times \dfrac{(x+y)(\cancel{x-y})}{(\cancel{m+n})(m+n)} \\\\& = \dfrac{x+y}{m+n}. \end{aligned}\)