\frac{\left(2^2+4\right)\left(2+2\right)}{2^2+2\cdot \:2+4}

asked by guest
on Sep 16, 2024 at 1:04 pm



You asked:

Evaluate the expression: \(\frac{\left({2}^{2} + 4\right) \cdot \left(2 + 2\right)}{{2}^{2} + 2 \cdot 2 + 4}\)

MathBot Answer:

\[\frac{\left({2}^{2} + 4\right) \cdot \left(2 + 2\right)}{{2}^{2} + 2 \cdot 2 + 4} = \frac{8}{3} = 2.\overline{6}\]

\[\begin{aligned}\frac{\left({2}^{2} + 4\right) \cdot \left(2 + 2\right)}{{2}^{2} + 2 \cdot 2 + 4}& = \left(2^{2} + 4\right) \cdot \left(2 + 2\right) \cdot \frac{1}{2^{2} + 2 \cdot 2 + 4}\\& = \left(4 + 4\right) \cdot \left(2 + 2\right) \cdot \frac{1}{2^{2} + 2 \cdot 2 + 4}\\& = 8 \cdot \left(2 + 2\right) \cdot \frac{1}{2^{2} + 2 \cdot 2 + 4}\\& = 8 \cdot 4 \cdot \frac{1}{2^{2} + 2 \cdot 2 + 4}\\& = 8 \cdot 4 \cdot \frac{1}{4 + 2 \cdot 2 + 4}\\& = 8 \cdot 4 \cdot \frac{1}{4 + 4 + 4}\\& = 8 \cdot 4 \cdot \frac{1}{8 + 4}\\& = 8 \cdot \frac{4}{12}\\& = \frac{8}{3}\end{aligned}\]

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