Addition and Subtraction of Algebraic Fractions

Recap of addition subtraction of algebraic fractions in secondary 2.

Express two algebraic fractions as a single fraction.

Addition

\(\begin{align} \frac{x+3}{6}+\frac{x}{2}&=\frac{x+3}{6}+\frac{3(x)}{6} \\& =\frac{x+3+3x}{6} \\& =\frac{4x+3}{6}\end{align}\)

Subtraction

\(\begin{align} \frac{2(3a-b)}{5}-\frac{2a+5b}{3}&=\frac{3(2)(3a-b)}{15}-\frac{5(2a+5b)}{15} \\& =\frac{6(3a-b)-5(2a+5b)}{15} \\& =\frac{18a-6b-10a-25b}{15} \\& =\frac{8a-31b}{15}\end{align}\)