The expression you provided in the image is as follows:

$\frac{2\sqrt{v^2} + 5\sqrt{v} + 2}{\sqrt{v}(1 - \sqrt{v})} \Big/ \left( \frac{1}{\sqrt{v^2}} + \frac{2}{\sqrt{v}} \right)$

To simplify this expression, let's break down the steps:

1. Rewrite the terms with square roots:
   We can simplify $\sqrt{v^2}$ as $v$ and $\frac{1}{\sqrt{v^2}}$ as $\frac{1}{v}$. Similarly, we rewrite $\sqrt{v}$ as is.

   So, the expression becomes: $\frac{2v + 5\sqrt{v} + 2}{\sqrt{v}(1 - \sqrt{v})} \Big/ \left( \frac{1}{v} + \frac{2}{\sqrt{v}} \right)$

2. Simplify the denominator of the fraction on the right:
   Combine the terms in $\frac{1}{v} + \frac{2}{\sqrt{v}}$ over a common denominator: $\frac{1}{v} + \frac{2}{\sqrt{v}} = \frac{1 + 2v^{1/2}}{v}$

   So, the entire expression now looks like this: $\frac{2v + 5\sqrt{v} + 2}{\sqrt{v}(1 - \sqrt{v})} \Big/ \frac{1 + 2\sqrt{v}}{v}$

3. Rewrite the complex fraction:
   Dividing by a fraction is the same as multiplying by its reciprocal. Thus: $\frac{2v + 5\sqrt{v} + 2}{\sqrt{v}(1 - \sqrt{v})} \times \frac{v}{1 + 2\sqrt{v}}$

4. Simplify by canceling terms if possible:
   Now, multiply the numerators and the denominators. However, further simplification would depend on whether we can factor terms like $2v + 5\sqrt{v} + 2$, which doesn’t factor neatly over integers.

Would you like me to proceed with further steps or have any particular questions?

Related Questions:

1. How do I factor expressions involving square roots?
2. Can you show examples of simplifying complex fractions step-by-step?
3. What are some techniques to handle nested fractions in algebra?
4. Could you explain simplifying expressions with radical terms further?
5. How do I multiply expressions with different square root terms?

Tip:

When simplifying complex fractions, try to rewrite them as a multiplication by the reciprocal—it often makes the simplification process much easier.