Answer:
x = 3
Step-by-step explanation:
[tex]\dfrac{7}{x-1}-\dfrac{5}{x}=\dfrac{11}{x^2-x}\\\\Domain:\\\\(x-1\neq0\ \wedge\ x\neq0\ \wedge\ x^2-x\neq0)\Rightarrow(x\neq-1\ \wedge\ x\neq1)\\===============================[/tex]
[tex]\dfrac{7}{x-1}-\dfrac{5}{x}=\dfrac{11}{x^2-x}\\\\\dfrac{7\cdot x}{(x-1)\cdot x}-\dfrac{5\cdot(x-1)}{x\cdot(x-1)}=\dfrac{11}{x^2-x}\\\\\dfrac{7x}{x^2-x}-\dfrac{5x-5}{x^2-x}=\dfrac{11}{x^2-x}\\\\\dfrac{7x-5x+5}{x^2-x}=\dfrac{11}{x^2-x}\\\\\dfrac{2x+5}{x^2-x}=\dfrac{11}{x^2-x}\iff2x+5=11\qquad\text{subtract 5 from both sides}\\\\2x=6\qquad\text{divide both sides by 2}\\\\x=3\in D[/tex]
