ll values of x: (1)/(x-1)-3=-(7x)/(x-1)

To solve the equation $\frac{1}{x-1} - 3 = -\frac{7x}{x-1}$, we can follow these steps:<br /><br />1. Multiply both sides of the equation by $(x-1)$ to eliminate the fractions:<br />$(x-1)\left(\frac{1}{x-1} - 3\right) = (x-1)\left(-\frac{7x}{x-1}\right)$<br /><br />2. Simplify the equation:<br />$1 - 3(x-1) = -7x$<br /><br />3. Distribute the $-3$ on the left side:<br />$1 - 3x + 3 = -7x$<br /><br />4. Combine like terms:<br />$4 - 3x = -7x$<br /><br />5. Add $3x$ to both sides:<br />$4 = -4x$<br /><br />6. Divide both sides by $-4$:<br />$x = -1$<br /><br />Therefore, the solution to the equation is $x = -1$.