Answer
$\dfrac{1}{7}x^{2}-\dfrac{1}{3}x+\dfrac{2}{3}$
Work Step by Step
$\Big(\dfrac{1}{3}x^{2}-\dfrac{2}{7}x\Big)-\Big(\dfrac{4}{21}x^{2}+\dfrac{1}{21}x-\dfrac{2}{3}\Big)$
Remove both parentheses. To remove the second one, change the sign of every term inside it:
$\dfrac{1}{3}x^{2}-\dfrac{2}{7}x-\dfrac{4}{21}x^{2}-\dfrac{1}{21}x+\dfrac{2}{3}=...$
Simplify by combining like terms:
$...=\Big(\dfrac{1}{3}-\dfrac{4}{21}\Big)x^{2}-\Big(\dfrac{2}{7}+\dfrac{1}{21}\Big)x+\dfrac{2}{3}=...$
$...=\dfrac{21-12}{63}x^{2}-\dfrac{42+7}{147}x+\dfrac{2}{3}=\dfrac{9}{63}x^{2}-\dfrac{49}{147}x+\dfrac{2}{3}=...$
$...=\dfrac{1}{7}x^{2}-\dfrac{1}{3}x+\dfrac{2}{3}$
