\displaystyle \dfrac{6x}{2}-\dfrac{7x}{2}	\displaystyle =	\displaystyle \frac{6x-7x}{2}	Subtract the numerators
	\displaystyle =	\displaystyle -\dfrac{x}{2}	Evaluate the subtraction

Example 2

Simplify the following: \dfrac{3x}{5}-\dfrac{x}{7}

Worked Solution

Create a strategy

Find a common denominator to add the fractions.

Apply the idea

5\times 7=35 so 35 is a common multiple of the denominators. So we need to multiply the numerator and denominator of each fraction by the other denominator.

\displaystyle \dfrac{3x}{5}-\dfrac{x}{7}	\displaystyle =	\displaystyle \frac{3x \times 7}{5 \times 7} - \frac{x \times 5}{7 \times 5}	Multiply fractions by the other denominator
	\displaystyle =	\displaystyle \frac{21x}{35}-\frac{5x}{35}	Evaluate the second fraction
	\displaystyle =	\displaystyle \frac{21x-5x}{35}	Subtract the numerators
	\displaystyle =	\displaystyle \frac{16x}{35}	Evaluate the subtraction

Example 3

Simplify the following: \dfrac{-3x-1}{6}+\dfrac{x+6}{6}

Worked Solution

Create a strategy

We can write the numerators together as a single expression over the common denominator.

Apply the idea

\displaystyle \dfrac{-3x-1}{6}+\dfrac{x+6}{6}	\displaystyle =	\displaystyle \dfrac{(-3x-1) + (x+6)}{6}	Add the numerators
	\displaystyle =	\displaystyle \dfrac{-3x+x-1+6}{6}	Collect like terms
	\displaystyle =	\displaystyle \dfrac{-2x+5}{6}	Subtract the numerator
	\displaystyle =	\displaystyle -\dfrac{2x+5}{6}	Simplify

Idea summary

The most important things to remember when adding and subtracting fractions:

We need like denominators.
We need to keep our fractions equivalent.

Outcomes

MA5.2-6NA

simplifies algebraic fractions, and expands and factorises quadratic expressions

2.03 Adding and subtracting algebraic fractions

Ideas

Addition and subtraction of algebraic fractions

Examples

Example 1

Example 2

Example 3

Outcomes

MA5.2-6NA

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