Algebra: Adding and subtracting fractions
Addition and subtraction of like fractions
Examples 

When adding like fractions, the #\blue{\text{denominator }}# remains equal and the #\orange{\text{numerators }}# are added. 
\[\begin{array}{rcl} \dfrac{\orange{2x}}{\blue{y}} + \dfrac{\orange{x}}{\blue{y}} &=& \dfrac{\orange{3x}}{\blue{y}} \\ \end{array}\] 
When subtracting like fractions, the #\blue{\text{denominator }}# remains equal and the #\orange{\text{numerators}}# are subtracted. 
\[\begin{array}{rcl}\dfrac{\orange{x}}{\blue{y}}  \dfrac{\orange{2x}}{\blue{y}} &=& \dfrac{\orange{x}}{\blue{y}} \end{array}\] 
Write as a single fraction and simplify as far as possible:
\[\dfrac{9}{x+7} + \dfrac{x}{x+7}\]
\[\dfrac{9}{x+7} + \dfrac{x}{x+7}\]
#{{x+9}\over{x+7}}#
#\begin{array}{rcl}
\dfrac{9}{x+7} + \dfrac{x}{x+7} &=& \dfrac{9 + x}{x+7}\\
&& \phantom{xxx}\blue{\text{like fractions added by adding numerators}}\\
&=& \dfrac{x+9}{x+7} \\ && \phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
#\begin{array}{rcl}
\dfrac{9}{x+7} + \dfrac{x}{x+7} &=& \dfrac{9 + x}{x+7}\\
&& \phantom{xxx}\blue{\text{like fractions added by adding numerators}}\\
&=& \dfrac{x+9}{x+7} \\ && \phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
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