How do you simplify (2x-10)/(3x - 21) and what are the restrictions?

1 Answer
May 30, 2015

$\frac{2 x - 10}{3 x - 21} = \frac{2 \left(x - 5\right)}{3 \left(x - 7\right)}$

$= \frac{2}{3} \left(\frac{\left(x - 7\right) + 2}{x - 7}\right)$

$= \frac{2}{3} \left(\frac{x - 7}{x - 7} + \frac{2}{x - 7}\right)$

$= \frac{2}{3} \left(1 + \frac{2}{x - 7}\right)$

$= \frac{2}{3} + \frac{4}{3 \left(x - 7\right)}$

The only restriction is $x \ne 7$