I values of x: (1)/(x-7)-1=-(9x)/(x-7)

To solve the equation $\frac{1}{x-7} - 1 = -\frac{9x}{x-7}$, we can follow these steps:<br /><br />1. Multiply both sides of the equation by $(x-7)$ to eliminate the fractions:<br />$(x-7)\left(\frac{1}{x-7} - 1\right) = (x-7)\left(-\frac{9x}{x-7}\right)$<br /><br />2. Simplify the equation:<br />$1 - (x-7) = -9x$<br /><br />3. Combine like terms:<br />$1 - x + 7 = -9x$<br /><br />4. Move all terms involving $x$ to one side of the equation:<br />$1 + 7 = -9x + x$<br /><br />5. Simplify the equation:<br />$8 = -8x$<br /><br />6. Divide both sides of the equation by $-8$ to solve for $x$:<br />$x = -1$<br /><br />Therefore, the value of $x$ that satisfies the equation is $x = -1$.