Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} + \frac{x-2}{x+2} = 3$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $(x-2)(x+3)+1=0$; $x=2$.

If $b=0$ and $c < 0$,is it true that the roots of $x^{2}+bx+c=0$ are numerically equal and opposite in sign? Justify.

At present,Asha's age (in $years$) is $2$ more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age,Asha's age would be one year less than $10$ times the present age of Nisha. Find the present ages of both Asha and Nisha (in $years$).

The roots of the quadratic equation $\ldots \ldots \ldots \ldots$ are $-4$ and $5$.

Find the roots of the following quadratic equations by the factorisation method:
$\frac{2}{5} x^{2}-x-\frac{3}{5}=0$