In rectangle $ABCD$,$AB + BC = 23$ and its area is $120$. If $AB > BC$,then $AB = \ldots$

Solve the following equation using the method of factorization: $6(2x+1)^2 - (2x+1) - 5 = 0$

$A$ cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was $3$ more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ $90,$ find the number of articles produced and the cost of each article.

Find the roots of the equation $2x^{2}-5x+3=0$ by factorisation.

Solve the following equation using the method of factorization and write its solution set: $\frac{x}{x+1} + \frac{x+1}{x} = \frac{5}{2}$

Solve the following equation using the method of factorization and write its solution set: $\frac{x}{x-1} + \frac{x-1}{x} = \frac{25}{12}$