Question

Find the root of the following equation x/x-1+x-1/x=85/42​

Answer 1

Answer:

x=7,-6

Step-by-step explanation:

if you mean the question is

$\frac{x}{x - 1} + \frac{x - 1}{x} = \frac{85}{42}$

then the answer is x=7, or x= -6

$a + \frac{1}{a} = \frac{85}{42} \: \: \: (suppose \: \frac{x}{x - 1} = a)$

$or \: \frac{ {a}^{2} + 1}{a} = \frac{85}{42}$

$or \: 42 {a}^{2} - 85a + 42 = 0$

$or \: 42 {a}^{2} - (49 + 36)a + 42 = 0$

$or \: (6 a- 7)(7a - 6) = 0$

$if \: (6a - 7) = 0 \: \: \: \: \: or \: (7a - 6) = 0$

$a = \frac{7}{6} \: \: \: \: \: or \: a = \frac{6}{7}$

$\frac{x}{x - 1} = \frac{7}{6} \: \: or \: \: \frac{x}{x - 1} = \frac{6}{7}$

$x = 7 \: \: or \: \: x = - 6$

Answer 2

Answer:

Answer in the attachment.

Step-by-step explanation:

ThAnK yOu!