The value of \(\left(2+\dfrac32\right)^2 - \left[4-\left(\dfrac63\right)^2\right] \div \dfrac12\) is
\(\tfrac{49}{2}\)
\(\left(2+\dfrac32\right)^2 = \left(\dfrac72\right)^2 = \dfrac{49}{4}\).
\(\left(\dfrac63\right)^2 = 2^2 = 4\), so the bracket \(4-4=0\).
The whole expression, taken together, is then divided by \(\tfrac12\): \(\dfrac{49}{4}\div\dfrac12 = \dfrac{49}{4}\times2 = \dfrac{49}{2}\).
Hence, the value of the expression is \(\tfrac{49}{2}\).
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