Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{4x-45}{x-9}+\frac{2x-9}{x-9}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6x-54}{x-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\end{aligned} $$ | |
① | To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{4x-45}{x-9} + \frac{2x-9}{x-9} & = \frac{4x-45}{\color{blue}{x-9}} + \frac{2x-9}{\color{blue}{x-9}} = \\[1ex] &=\frac{ 4x-45 + \left( 2x-9 \right) }{ \color{blue}{ x-9 }}= \frac{6x-54}{x-9} \end{aligned} $$ |
② | Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-9}$. $$ \begin{aligned} \frac{6x-54}{x-9} & =\frac{ 6 \cdot \color{blue}{ \left( x-9 \right) }}{ 1 \cdot \color{blue}{ \left( x-9 \right) }} = \\[1ex] &= \frac{6}{1} =6 \end{aligned} $$ |