1. **Simplify the expression:** Given $$\frac{\frac{6}{x} - \frac{1}{x}}{\frac{5}{x} - \frac{9}{x}}$$ Combine the terms in numerator and denominator: $$\frac{\frac{6 - 1}{x}}{\frac{5 - 9}{x}} = \frac{\frac{5}{x}}{\frac{-4}{x}}$$ Since denominators are the same ($x$), they cancel: $$\frac{5/x}{-4/x} = \frac{5}{x} \times \frac{x}{-4} = \frac{5}{-4} = -\frac{5}{4}$$ So the simplified expression equals $$-\frac{5}{4}$$. 2. **Solve for x in equation:** $$x^2 + 2x - 8 = 0$$ Use quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, \text{ where } a=1, b=2, c=-8$$ Calculate discriminant: $$\Delta = 2^2 - 4\times1\times(-8) = 4 + 32 = 36$$ Therefore: $$x = \frac{-2 \pm \sqrt{36}}{2} = \frac{-2 \pm 6}{2}$$ Two roots: $$x_1 = \frac{-2 + 6}{2} = 2$$ $$x_2 = \frac{-2 - 6}{2} = -4$$ 3. **Matrix addition problem:** Given matrices $$A=\begin{pmatrix} -1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}, \quad B=\begin{pmatrix} 0 & 1 \\ 2 & 3 \\ 4 & 5 \end{pmatrix}$$ Check if matrices can be added: matrix addition requires same dimensions. Here, - Matrix A is 3x3 - Matrix B is 3x2 Because dimensions differ, matrix addition is **impossible**. Answer: (iv) অসম্ভব (impossible). **Final answers:** - Simplified fraction expression: $-\frac{5}{4}$ - Solutions for $x$: $2$ and $-4$ - Matrix addition $A + B$ is impossible.