Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{1}{x-2}-\frac{2}{x^2-2x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x-2}{x^2-2x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{x}\end{aligned} $$ | |
① | To subtract raitonal expressions, both fractions must have the same denominator. |
② | Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-2}$. $$ \begin{aligned} \frac{x-2}{x^2-2x} & =\frac{ 1 \cdot \color{blue}{ \left( x-2 \right) }}{ x \cdot \color{blue}{ \left( x-2 \right) }} = \\[1ex] &= \frac{1}{x} \end{aligned} $$ |