Solve the equation (x)/(5x-25)-9=(1)/(x-5) If there is more than one correct answer.enter your answers as a comma separated list.If there is no solution, enter "none". x=square

To solve the equation $\frac {x}{5x-25}-9=\frac {1}{x-5}$, we can start by simplifying the equation.<br /><br />First, let's multiply both sides of the equation by $(5x-25)(x-5)$ to eliminate the denominators:<br /><br />$(5x-25)(x-5)\left(\frac {x}{5x-25}-9\right)=(5x-25)(x-5)\left(\frac {1}{x-5}\right)$<br /><br />Simplifying the left side of the equation, we have:<br /><br />$x(x-5)-9(5x-25)(x-5)=5x-25$<br /><br />Expanding and simplifying further, we get:<br /><br />$x^2-5x-45x+225=5x-25$<br /><br />Combining like terms, we have:<br /><br />$x^2-50x+225=5x-25$<br /><br />Rearranging the equation, we get:<br /><br />$x^2-55x+250=0$<br /><br />Now, we can solve this quadratic equation by factoring or using the quadratic formula. Let's try factoring first:<br /><br />$(x-25)(x-30)=0$<br /><br />Setting each factor equal to zero, we have:<br /><br />$x-25=0$ or $x-30=0$<br /><br />Solving for $x$, we get:<br /><br />$x=25$ or $x=30$<br /><br />Therefore, the solutions to the equation are $x=25$ and $x=30$.