We have seen how to add and subtract similar fractions. Next to that, we have seen how to make two fractions similar. We can use this to add and subtract dissimilar fractions.
If we want to add two dissimilar fractions, we can follow the following steps.
 Make the two fractions similar.
 Add the two similar fractions.
 Simplify the fractions if possible.
Subtracting works the same way.
 Make the two fractions similar.
 Subtract the two similar fractions.
 Simplify the fractions if possible.

Examples
\[\begin{array}{rcl} {\dfrac{\orange{2}}{\blue{x}}+\dfrac{\purple{3}}{\green{y}} } &{=}& {\dfrac{\orange{2} {\green{y}}}{\blue{x} {\green{y}}}+\dfrac{\purple{3} {\blue{x}}}{{\blue{x}} \green{y}}} \\ &{=}& {\dfrac{\orange{2} \green{y} + \purple{3} \blue{x}}{\blue{x} \green{y}}} \\ \\ {\dfrac{\orange{2}}{\blue{x}}\dfrac{\purple{3}}{\green{y}}} &{=}& {\dfrac{\orange{2} {\green{y}}}{\blue{x} {\green{y}}}\dfrac{\purple{3} {\blue{x}}}{{\blue{x}} \green{y}}} \\ &{=}& {\dfrac{\orange{2} \green{y}  \purple{3} \blue{x}}{\blue{x} \green{y}}} \end{array}\]

Just as when subtracting similar fractions, when subtracting dissimilar fractions, we need to place brackets around the second denominator.

Example
\[\begin{array}{rcl} && {\dfrac{\orange{6}}{\blue{x+1}}\dfrac{\purple{1}}{\green{x}}} \\ &{=}& {\dfrac{\orange{6 } {\green{x}}}{{\green{x}} \blue{ (x+1)}}\dfrac{{\blue{x+1}}}{\green{x} {\blue{(x+1)}}}} \\ &{=}& {\dfrac{\orange{6} \green{ x}  \blue{\left(x+1\right)}}{\green{x} \blue{(x+1)}}} \\ &{=}& { \dfrac{{\orange{6} \green{x}  x 1}}{\green{x} \blue{(x+1)}}} \\ &{=}& { \dfrac{{5 x1}}{\green{x} \blue{(x+1)}}}\end{array}\]

Write as a single fraction and simplify as much as possible:
\[6 + \dfrac{x\cdot y}{9}\]
#6 + \dfrac{x\cdot y}{9}=# #{{x\cdot y+54}\over{9}}#
#\begin{array}{rcl}
6 + \dfrac{x\cdot y}{9} &=& \dfrac{(6) \cdot 9}{(1) \cdot 9} + \dfrac{(x\cdot y) \cdot 1}{(9) \cdot 1} \\
&& \phantom{xxx}\blue{\text{fractions put over the same denominator}}\\
&=& \displaystyle {{x\cdot y+54}\over{9}}
\\ && \phantom{xxx}\blue{\text{similar fractions added}}\\
\end{array}#