Question

How to solve this problem with the steps​

Answer 1

x = 3

Explanation:

`(7)/(x-1)-(5)/(x)=(11)/(x^2-x)\\\\Domain:\\\\(x-1\\eq0\ \wedge\ x\\eq0\ \wedge\ x^2-x\\eq0)\Rightarrow(x\\eq-1\ \wedge\ x\\eq1)\\===============================`

`(7)/(x-1)-(5)/(x)=(11)/(x^2-x)\\\\(7\cdot x)/((x-1)\cdot x)-(5\cdot(x-1))/(x\cdot(x-1))=(11)/(x^2-x)\\\\(7x)/(x^2-x)-(5x-5)/(x^2-x)=(11)/(x^2-x)\\\\(7x-5x+5)/(x^2-x)=(11)/(x^2-x)\\\\(2x+5)/(x^2-x)=(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`