Question

if x=6/x-5
, then x lies in the interval​

Answer 1

Answer:

$x = 6, (-1)$

Step-by-step explanation:

Given: $x = \frac{6}{x-5}$

By cross multiplication and solving fractions:

                   $x^{2} - 5x = 6$

                   $x^{2} - 5x - 6 = 0$

By splitting the middle term: $x^{2} - 6x + x - 6 = 0$

Taking the x term common: $x(x - 6) + 1(x - 6) = 0$

Taking (x-6) common: $(x - 6) (x + 1) = 0$

so, $x = 6, (-1)$