13.06 Adding and subtracting algebraic fractions
Simplify:
\dfrac{2 x}{7} + \dfrac{7 x}{7}
\dfrac{3x}{4}+\dfrac{2x}{4}
\dfrac{2 x}{3} + \dfrac{10 x}{3}
\dfrac{3 x}{12} + \dfrac{12 x}{12}
\dfrac{-8 x}{9} + \dfrac{4x}{9}
\dfrac{-3 x}{14} + \dfrac{- 2x}{14}
\dfrac{8 x}{2} - \dfrac{3 x}{2}
\dfrac{13x}{3}-\dfrac{8x}{3}
\dfrac{7 x}{5} - \dfrac{10 x}{5}
\dfrac{31 x}{6} - \dfrac{7 x}{6}
\dfrac{25 x}{24} - \dfrac{5 x}{24}
Simplify:
\dfrac{2 x}{3} + \dfrac{x + 3}{3}
\dfrac{7 x}{8} + \dfrac{5 x + 2}{8}
\dfrac{-2 x}{7} + \dfrac{4 x - 3}{7}
\dfrac{4 x - 10}{3} + \dfrac{- 5 x + 10}{3}
\dfrac{-6 x - 8}{5} + \dfrac{- 3 x -5}{5}
\dfrac{2 x^2 - 3}{5} + \dfrac{3 x^2 + 6}{5}
\dfrac{-5 x^2 - 2x }{3} + \dfrac{- 3 x^2 -2x}{3}
Find the lowest common denominator for the following pairs of algebraic fractions:
\dfrac{w}{2} and \dfrac{w}{6}
\dfrac{s}{3} and \dfrac{s}{6}
\dfrac{x}{2} and \dfrac{y}{3}
\dfrac{r}{5} and \dfrac{s}{3}
Consider the algebraic fractions \dfrac{2 m}{5} and \dfrac{3 m}{6}.
Find the lowest common denominator.
Hence, simplify \dfrac{2 m}{5} + \dfrac{3 m}{6}.
Complete the following:
\dfrac{3x}{5}+\dfrac{2x}{⬚}=\dfrac{⬚}{35}Simplify:
\dfrac{2 x}{5} + \dfrac{4 x}{7}
\dfrac{2 x}{14} + \dfrac{14 x}{21}
\dfrac{4 x}{45} - \dfrac{x}{18}
- 9 x - \dfrac{5 x}{7}
\dfrac{3 x}{5} - \dfrac{2 x}{7}
-3x-\dfrac{3x}{8}
\dfrac{11x}{14}+\dfrac{7x}{21}
\dfrac{x}{15}+\dfrac{3x}{35}
Simplify:
\dfrac{2 x}{3} + \dfrac{2 x + 5}{9}
\dfrac{8 x}{13} + \dfrac{3 x + 4}{39}
\dfrac{3 x}{10} - \dfrac{4 x + 3}{16}
\dfrac{4x}{9}+\dfrac{2x-3}{36}
\dfrac{8 x}{11} - \dfrac{2 x - 3}{44}
\dfrac{y}{10}-\dfrac{5y+1}{25}
\dfrac{7 x}{8} - \dfrac{5 x + 6}{20}
\dfrac{x + 3}{3} + \dfrac{3 x - 2}{12}
\dfrac{x + 3}{3} - \dfrac{5 x - 7}{12}
\dfrac{2 x + 3}{4} - \dfrac{2 x + 2}{12}
\dfrac{5 x + 8}{6} + \dfrac{x + 2}{2}
\dfrac{3 x + 4}{6} + \dfrac{3 x + 4}{5}
\dfrac{2x+2}{4}-\dfrac{x+3}{8}
\dfrac{6x+7}{3}-\dfrac{3x-5}{9}
\dfrac{6 x^{2}}{7} + \dfrac{x^{2} + 5 x}{21}
\dfrac{2x^2}{7}+\dfrac{3x^2+2x}{28}
Simplify:
Simplify:
\dfrac{5}{x} + \dfrac{7}{x}
\dfrac{8}{3y} + \dfrac{10}{2y}
\dfrac{5 x - y}{x - 4} + \dfrac{x - 6 y}{4 - x}
\dfrac{5 x}{7 \left(x + 1\right)} - \dfrac{10}{x + 1}
\dfrac{1}{5} + \dfrac{7}{x - 6}
\dfrac{2 y + 5}{y - 3} - \dfrac{y + 3}{y - 3}
\dfrac{2}{\left(x + 3\right)} + \dfrac{5}{ \left(x + 5\right)}
\dfrac{x}{x-4} - \dfrac{12}{x + 4}
\dfrac{x^{2} }{x+4} - \dfrac{2}{x - 8}
\dfrac{11 x}{x-2} - \dfrac{x + 5}{x+8}