Solve for all values of x.

Question

x, minus, start fraction, 1, divided by, x, minus, 1, end fraction, equals, start fraction, 5, divided by, x, minus, 1, end fraction
x−
x−1
1
​
=
x−1
5
​

Answer 1

To solve for all values of x, we can cross multiply and solve for x.

\[(x-1) \cdot \frac{1}{x-1} = \frac{5}{x-1}\]
\[1 = \frac{5}{x-1}\]

Cross multiplying, we get:
\[x - 1 = 5\]
\[x = 6\]

Therefore, the solution to the equation is x = 6.