Solve the following equation using the method of factorization: $x + 3 + \frac{2}{x} = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $2kx^2 - 8x + k = 0$.

If Zeba were younger by $5\, \text{years}$ than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now? (in $\text{years}$)

The denominator of a non-zero ratio is one less than twice the numerator. If the sum of the ratio and its reciprocal is $2 \frac{4}{15},$ find the ratio.

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} - \frac{x-1}{x+1} = \frac{5}{x}$

If the value of the discriminant of a quadratic equation $6x^{2}-x-k=0$ is $25$,then $k = \ldots$