Question

solve it by factorization​

Answer 1

$\mathfrak{here \: is \: you r \: answer} \\ \frac{1}{x - 1} + \frac{1}{x - 4} = \frac{5}{4} \\ \frac{x - 4 + x - 1}{(x - 1)(x - 4)} = \frac{5}{4} \\ \frac{2x - 5}{x(x - 4) - 1( x- 4)} = \frac{5}{4} \\ \frac{2x - 5}{ {x}^{2} - 4x - x + 4} = \frac{5}{4} \\ \frac{2x - 5}{ {x}^{2} - 5x + 4 } = \frac{5}{4} \\ 4(2x - 5) = 5( {x}^{2} - 5x + 4) \\ 8x - 20 = 5 {x}^{2} - 25x + 20 \\ 20 + 20 = 5 {x}^{2} - 25x - 8x \\ 40 = 5 {x}^{2} - 33x \\ 5 {x}^{2} - 33x - 40 = 0$

Solve the above equation by any method you will be get the answer.