Question

3x-4upon7+7upon3x-4=5upon2

Answer 1

$\frac{3x - 4}{7} + \frac{7}{3x - 4} = \frac{5}{2}$

$\frac{(3x - 4)(3x - 4) + 49}{7(3x - 4)} = \frac{5}{2} \\ \\ \frac{ ({9x}^{2}-24x + 16) + 49}{21x - 28} = \frac{5}{2} \\ \\ \frac{ {9x}^{2} - 24x + 16 + 49}{21x - 28} = \frac{5}{2} \\ \\ \frac{ {9x}^{2} - 24x + 65}{21x - 28} = \frac{5}{2}$

$\frac{9x^2-(39 - 15)x + 65}{21x - 28} = \frac{5}{2} \\ \\ \frac{ {9x}^{2} - 39x + 15x + 65 }{21x - 28} = \frac{5}{2} \\ \\ \frac{3x(3x + 5) - 13(3x + 5)}{21x - 28} = \frac{5}{2} \\ \\ \frac{(3x + 5)(3x - 13)}{21x - 28} = \frac{5}{2} \\ \\ \frac{2(3x + 5)(3x - 13)}{5(21x - 28)} = 0$