Addition and subtraction with common denominator:
$\dfrac{\color{#026fc1}{P}}{\color{#c1026f}{Q}} + \dfrac{\color{#026fc1}{R}}{\color{#c1026f}{Q}} = \dfrac{\color{#026fc1}{P} + \color{#026fc1}{R}}{\color{#c1026f}{Q}} \qquad $ \t
\\
\\ $\dfrac{\color{#026fc1}{P}}{\color{#c1026f}{Q}} - \dfrac{\color{#026fc1}{R}}{\color{#c1026f}{Q}} = \dfrac{\color{#026fc1}{P} - \color{#026fc1}{R}}{\color{#c1026f}{Q}} \qquad $ \t
Notes
1.
As with ordinary fractions, this formula works only when the two expressions have the same denominator.
2.
When adding or subtracting expressions with the same denominator, do not factor or cancel before starting as you would with products or quotients; just leave them as they are until
after doing the addition or subtractions.
#[Examples][Ejemplos]#
\\ $\dfrac{\color{#026fc1}{y}}{\color{#c1026f}{xy+1}} + \dfrac{\color{#026fc1}{x-1}}{\color{#c1026f}{xy+1}} $ \t ${}= \dfrac{\color{#026fc1}{y + x - 1}}{\color{#c1026f}{xy+1}}$ \t
\\ \t
\\ $\dfrac{\color{#026fc1}{x^2+1}}{\color{#c1026f}{x-1}} - \dfrac{\color{#026fc1}{2x}}{\color{#c1026f}{x-1}} $ \t ${}= \dfrac{\color{#026fc1}{x^2-2x+1}}{\color{#c1026f}{x-1}}$ \t
\\ \t ${}= \dfrac{(x-1)^2}{x-1}$ \t
\\ \t ${}= x-1$ \t $\color{#6968d0}{(x-1)}$.