Question

Solve for all values of x:
start fraction, 6, x, divided by, x, minus, 1, end fraction, minus, 4, equals, start fraction, 6, divided by, x, minus, 1, end fraction
x−1
6x
​
−4=
x−1
6

Answer 1

Solve (6x)/(x−1) − 4 = 6/(x−1). Domain: x ≠ 1.

Multiply both sides by x−1:
6x − 4(x−1) = 6.

Expand and simplify:
6x − 4x + 4 = 6
2x + 4 = 6
2x = 2
x = 1,

but x = 1 is not allowed (denominator zero). Substituting any other x leads to a contradiction (the equation reduces to 6 = 4). Therefore there are no solutions.