Question

Rút gọn các biểu thức sau, rồi tính giá trị của chúng:

\(\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{6}\right)^2:\left(3\dfrac{1}{2}-1\dfrac{1}{6}\right)^2\)
 

Answer 1

\(=\left(\dfrac{5}{6}-\dfrac{1}{6}\right)^2:\left(\dfrac{7}{2}-\dfrac{7}{6}\right)^2\)

\(=\dfrac{4}{9}:\left(\dfrac{21}{6}-\dfrac{7}{6}\right)^2\)

\(=\dfrac{4}{9}:\left(\dfrac{7}{3}\right)^2=\dfrac{4}{9}:\dfrac{49}{9}=\dfrac{4}{49}\)

Answer 2

\(\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{6}\right)^2:\left(3\dfrac{1}{2}-1\dfrac{1}{6}\right)^2\)

\(=\left(\dfrac{5}{6}-\dfrac{1}{6}\right)^2:\left(\dfrac{7}{2}-\dfrac{7}{6}\right)^2\)

\(=\left(\dfrac{2}{3}\right)^2:\left(\dfrac{7}{3}\right)^2\)

\(=\dfrac{4}{9}:\dfrac{49}{9}\)

\(=\dfrac{9}{49}\)