Question

Solve for x1" title=" \frac{x}{a} = \frac{x}{b} " alt=" \frac{x}{a} = \frac{x}{b} " align="absmiddle" class="latex-formula">

Answer 1

$Domain:\ a\neq0\ \wedge\ b\neq0$

$\dfrac{x}{a}=\dfrac{x}{b}\qquad|\text{cross multiply}\\\\bx=ax\qquad|\text{subtract ax from both sides}\\\\bx-ax=0\\\\x(b-a)=0\qquad|\text{divide both sides by }\ b-a\neq0\\\\x=0$

$\dfrac{x}{a}=\dfrac{x}{b}\\\\if\ a\neq b\ then\ x=0\\\\if\ a=b\ then\ x\in\mathbb{R}$