Question

`(y)/(a) -b=(y)/(b) -a`
If a doesn't equals b
Find a, b, and y

Answer 1

`Domain:\ a\\eq0\ \wedge\ b\\eq0\\\\(y)/(a)-b=(y)/(b)-a\qquad\text{multiply both sides by ab}\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\\\\(b-a)y=ab(b-a)\qquad\text{divide both sides by}\ (a-b)\\eq0\\\\y=ab\\\\Answer:\ a\in\mathbb{R}-\{0\},\ b\in\mathbb{R}-\{0\},\ a\\eq b,\ y=ab\\\\Example:\\a=2,\ b=3\to y=(2)(3)=6\\\\substitute\ to\ the\ equation:\\\\L_s=(6)/(2)-3=3-3=0\\R_s=(6)/(3)-2=2-2=0\\\\L_s=R_s`