(3sqrt (2)+2sqrt (50)-sqrt (200))/(sqrt (8)sqrt (8)-2sqrt (32))

To simplify the given expression, we can start by simplifying the terms inside the numerator and denominator.

In the numerator, we have:
$3\sqrt{2} + 2\sqrt{50} - \sqrt{200}$

We can simplify $\sqrt{50}$ by factoring out the perfect square trinomial:
$\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$

Similarly, we can simplify $\sqrt{200}$ by factoring out the perfect square trinomial:
$\sqrt{200} = \sqrt{100 \cdot 2} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2}$

Substituting these simplified terms back into the numerator, we get:
$3\sqrt{2} + 2(5\sqrt{2}) - 10\sqrt{2} = 3\sqrt{2} + 10\sqrt{2} - 10\sqrt{2} = 3\sqrt{2}$

In the denominator, we have:
$\sqrt{8}\sqrt{8} - 2\sqrt{32}$

We can simplify $\sqrt{8}\sqrt{8}$ by recognizing that $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$:
$2\sqrt{8}\sqrt{8} = 2(2\sqrt{2})(2\sqrt{2}) = 8(2) = 16$

Similarly, we can simplify $\sqrt{32}$ by recognizing that $\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}$:
$2\sqrt{32} = 2(4\sqrt{2}) = 8\sqrt{2}$

Substituting these simplified terms back into the denominator, we get:
$2\sqrt{8}\sqrt{8} - 2\sqrt{32} = 16 - 8\sqrt{2} = 16 - 8\sqrt{2}$

Now, we can substitute the simplified numerator and denominator back into the original expression:
$\frac{3\sqrt{2} + 2\sqrt{50} - \sqrt{200}}{\sqrt{8}\sqrt{8} - 2\sqrt{32}} = \frac{3\sqrt{2}}{16 - 8\sqrt{2}}$

To simplify further, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
$\frac{3\sqrt{2}}{16 - 8\sqrt{2}} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \frac{3\sqrt{2}}{(16 + 8\sqrt{2})} = \