Question

Solve for x: -10x/2+x=x+8/x

Answer 1

$The\ domain:\\D:\ x\neq-2\ \wedge\ x\neq0\\\\\dfrac{-10x}{2+x}=\dfrac{x+8}{x}\ \ \ \ |\text{cross multiply}\\\\(-10x)(x)=(2+x)(x+8)\\\\-10x^2=(2)(x)+(2)(8)+(x)(x)+(x)(8)\\\\-10x^2=2x+16+x^2+8x\\\\-10x^2=x^2+10x+16\ \ \ +10x^2\\\\11x^2+10x+16=0\\\\a=11,\ b=10,\ c=16\\\\b^2-4ac=10^2-4(11)(16)=100-704=-604 < 0\\\\NO\ REAL\ SOLUTION$