Question
Answer
$$\dfrac{x(x+1)-30}{x^2+5x-6}=\dfrac{x-5}{x-1}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{x(x+1)-30}{x^2+5x-6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x^2+x-30}{x^2+5x-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x-5}{x-1}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x+1\right) $ $$ \color{blue}{x} \cdot \left( x+1\right) = x^2+x $$ |
| ② | Simplify $ \dfrac{x^2+x-30}{x^2+5x-6} $ to $ \dfrac{x-5}{x-1} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x+6}$. $$ \begin{aligned} \frac{x^2+x-30}{x^2+5x-6} & =\frac{ \left( x-5 \right) \cdot \color{blue}{ \left( x+6 \right) }}{ \left( x-1 \right) \cdot \color{blue}{ \left( x+6 \right) }} = \\[1ex] &= \frac{x-5}{x-1} \end{aligned} $$ |
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Simplify Rational Expressions