Question

please give me solution of this ​

Answer 1

$x = 5 \: \: and \: \: \frac{5}{2}$

Step-by-step explanation:

$Given, \: \: \: \frac{2x - 3}{x - 2} + \frac{2x - 7}{x - 4} = 5 \frac{1}{3} \\ \frac{(2x - 3)(x - 4) + (2x - 7)(x - 2)}{(x - 2)(x - 4)} = \frac{16}{3} \\ \frac{2 {x}^{2} - 11x + 12 + 2 {x}^{2} - 11x + 14 }{(x - 2)(x - 4)} = \frac{16}{3} \\ \frac{4 {x}^{2} - 22x + 26 }{ {x}^{2} - 6x + 8 } = \frac{16}{3} \\ 3(4 {x}^{2} - 22x + 26) = 16({x}^{2} - 6x + 8) \\ 12 {x}^{2} - 66x + 78 = 16 {x}^{2} - 96x + 128 \\ 12 {x}^{2} - 66x + 78 - 16 {x}^{2} + 96x - 128 = 0 \\ - 4 {x}^{2} + 30x - 50 = 0 \\ - 2(2 {x}^{2} - 15x + 25 ) = 0 \\ 2 {x}^{2} - 15x + 25 = 0 \\ 2 {x}^{2} - 10x - 5x + 25 = 0 \\ 2x(x - 5) - 5(x - 5) = 0 \\ (x - 5)(2x - 5) = 0 \\ x - 5 = 0 \: \: \: and \: \: \: 2x - 5 = 0 \\ x = 5 \: \: \: and \: \: \: 2x = 5 \\ x = 5 \: \: \: and \: \: \: x = \frac{5}{2}$