Multiple Choice 10 points Solve: (9x)/(x-9)-(4)/(x)=(36)/(x^2)-9x x=9 x=(4)/(9) x=0 x=6

Rewrite the equation with the LCD$x (x-9)$ <br />$\displaystyle \frac{9x^2}{x(x-9)}-\frac{4(x-9)}{x(x-9)}=\frac{36}{x(x-9)}$ <br />Eliminate the denominator<br />$9x^2-4(x-9)=36$ <br />Expand the parentheses<br />$9x^2-4x+36=36$ <br />Regroup like terms<br />$9x^2-4x=0$ <br />Factorize the equation<br />$x(9x-4)=0$ <br />Find roots of qudratic equation<br />$x=0 \ or \ 9x-4=0$ <br />Solve for $x$ <br />$x_{1}=0,x_{2}=\frac{4}{9}$ <br />Since the denominator can't be $0$, the domain of$x$ is<br />$x\ne9, x\ne0$ <br />Find the intersection between the solution and the domain of$x$ <br />$x=\frac{4}{9}$ <br />