Adding and Subtracting Algebraic Fractions
Grade 7You always need a common denominator
Just like 1/3 + 1/4 needs a common denominator of 12, algebraic fractions need a common denominator before you can add or subtract them. The common denominator is usually the product of the two separate denominators (or their LCM if they share factors).
Worked example
EXAMPLE
Write as a single fraction: 3/(x + 1) + 2/(x − 2)
Common denominator: (x + 1)(x − 2). Rewrite each fraction: 3(x − 2) / [(x + 1)(x − 2)] + 2(x + 1) / [(x + 1)(x − 2)]. Combine tops: 3(x − 2) + 2(x + 1) = 3x − 6 + 2x + 2 = 5x − 4. Answer: (5x − 4) / [(x + 1)(x − 2)].
Expanding the numerator carefully
When subtracting fractions, the minus sign applies to the whole numerator of the second fraction — not just the first term. Put brackets around it before you expand, or you will drop a sign.
Try this one
Work out the value of \( \dfrac{y}{2} + \dfrac{y}{5} \) when \( y = 3.5 \).
[3]
Nova's hint:
Try to Solve it with Nova?
This is substituting a value into a sum of two algebraic fractions.
Ask yourself: 'is it easier to work out each fraction separately and then add?' For instance, for \( \dfrac{t}{2}+\dfrac{t}{4} \) you could evaluate each term first, then combine.
