Solve for x (x)/(a) = (x)/(b)

Question

Solve for x

`(x)/(a) = (x)/(b)`

Answer 1

`Domain:\ a\\eq0\ \wedge\ b\\eq0`

`(x)/(a)=(x)/(b)\qquad|\text{cross multiply}\\\\bx=ax\qquad|\text{subtract ax from both sides}\\\\bx-ax=0\\\\x(b-a)=0\qquad|\text{divide both sides by }\ b-a\\eq0\\\\x=0`

`(x)/(a)=(x)/(b)\\\\if\ a\\eq b\ then\ x=0\\\\if\ a=b\ then\ x\in\mathbb{R}`