Question
Answer
$$\dfrac{6a^2+5a-6}{3a^2-5a+2}=\dfrac{2a+3}{a-1}$$
Explanation
| $$ \begin{aligned}\frac{6a^2+5a-6}{3a^2-5a+2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2a+3}{a-1}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{6a^2+5a-6}{3a^2-5a+2} $ to $ \dfrac{2a+3}{a-1} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{3a-2}$. $$ \begin{aligned} \frac{6a^2+5a-6}{3a^2-5a+2} & =\frac{ \left( 2a+3 \right) \cdot \color{blue}{ \left( 3a-2 \right) }}{ \left( a-1 \right) \cdot \color{blue}{ \left( 3a-2 \right) }} = \\[1ex] &= \frac{2a+3}{a-1} \end{aligned} $$ |
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Simplify Rational Expressions