Question

Solve x/2+1/2= x - 3 + 5/x

Answer 1

`\cfrac{x}{2}+\cfrac{1}{2}=x-3+\cfrac{5}{x}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2x}}{2x\left( \cfrac{x}{2}+\cfrac{1}{2} \right)~~ = ~~2x\left( x-3+\cfrac{5}{x} \right)} \\\\\\ x^2+x=2x^2-6x+10\implies x=x^2-6x+10\implies 0=x^2-7x+10 \\\\\\ 0=(x-5)(x-2)\implies x= \begin{cases} 5\\ 2 \end{cases}`