To solve the inequalities in the image you provided, let’s break them down step by step.

### Inequality 1:
1. \( \frac{2x^2 + 3}{(x-1)} > \frac{4x^2}{(x+2)} \)

To solve this, first, we find a common denominator and cross-multiply where applicable. Rearranging the terms will help in identifying critical points for further analysis.

### Inequality 2:
2. \( \frac{2x^2 + 3}{4} - 1 < \frac{x^2 + x - 2}{3} \)

Similarly, we can start by multiplying through by a common denominator (which is 12) to eliminate the fractions. After simplifying, we will isolate \(x\) and solve for it.

### Inequality 3:
3. \( 3y(2x-1)(x-5) > 0 \)

Here, we will analyze the expression to find the critical points by setting it to zero. We can determine the ranges of \(y\) for which the product is positive.

### Steps for General Solution:
1. Determine critical points for each inequality.
2. Test intervals defined by the critical points to see where the inequalities hold true.
3. Express the solution sets in interval notation or as inequalities.

If you would like a more detailed solution for each inequality, please let me know!