GENERAL DIRECTION: ALWAYS SHOW COMPLETE AND DETAILED SOLUTION. BOX YOUR FINAL ANSWER. Solve and check. The equation presented is as follows:\[4. \quad \frac{5}{n} - \frac{6}{n^3 - 2n^2} = \frac{n^2 + 5n - 6}{n^3 - 2n^2}\]This equation features two fractions being subtracted on the left-hand side. The first fraction has a numerator of 5 and a denominator of \(n\). The second fraction has a numerator of 6 and a denominator of \(n^3 - 2n^2\). The right-hand side is a single fraction with a numerator of \(n^2 + 5n - 6\) and a denominator of \(n^3 - 2n^2\). The equation is shown to be balanced, suggesting that the expression on the left equals the expression on the right. **Equation 5:**\[\frac{1}{2} = \frac{x^2 - 7x + 10}{4x} - \frac{1}{2x}\]**Explanation:** This equation involves rational expressions and operations. The left side is a simple fraction, while the right side involves two fractions with polynomial numerators and linear denominators.**Equation 6:**\[\frac{a^2 - 4a - 12}{a^2 - 10a + 25} = \frac{6}{a-5} + \frac{a-3}{a-5}\]**Explanation:** This equation features a complex fraction equated to the sum of two simpler fractions. The numerators are polynomials, and the denominators involve factored quadratic expressions. Simplifying or solving such equations typically requires factoring and finding a common denominator.

We are authorized to answer one question at a time, since you have not mentioned which question you are looking for, so we are answering the first one, please repost your other questions if you want to get answered. 4. Consider 5n-6n3-2n2=n2+5n-6n3-2n2