Question

find the value of x in the equation 2/x-3+3/x-4=5/x​

Answer 1

Step-by-step explanation:

$\frac{2}{x - 3} + \frac{3}{x - 4} = \frac{5}{x}$

$\frac{2(x - 4) + 3(x - 3)}{(x - 3)(x - 4)} = \frac{5}{x}$

$\frac{2x - 8 + 3x - 9}{ {x}^{2} - 4x - 3x + 12} = \frac{5}{x}$

$\frac{5x - 17}{ {x}^{2} - 7x + 12} = \frac{5}{x}$

$5( {x}^{2} - 7x + 12) = x(5x - 17)$

$5 {x}^{2} - 35x + 60 = 5 {x}^{2} - 17x$

$- 35x + 17x = - 60$

$- 18x = - 60$

$x = \frac{60}{18}$

$x = \frac{10}{3}$