Question

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1/x + 1/3x^2 = 1/3x


A) { -1/2}

B) { 6}

C) { -13/6, 1/2}

D) {1/2}

Answer 1

`Domain:\ x\\eq0\\\\(1)/(x)+(1)/(3x^2)=(1)/(3x)\\\\(1\cdot3x)/(x\cdot3x)+(1)/(3x^2)=(1)/(3x)\\\\(3x)/(3x^2)+(1)/(3x^2)=(1)/(3x)\\\\(3x+1)/(3x^2)=(1)/(3x)\qquad\text{cross multiply}\\\\(3x)(3x+1)=(3x^2)(1)\qquad\text{use distributive property}\\\\(3x)(3x)+(3x)(1)=3x^2\\\\9x^2+3x=3x^2\qquad\text{subtract}\ 3x^2\ \text{from both sides}\\\\6x^2+3x=0\\\\3x(2x+1)=0\iff3x=0\ \vee\ 2x+1=0\\\\3x=0\qquad\text{divide both sides by 3}\\x=0\\otin Domain`

`2x+1=0\qquad\text{subtract 1 from both sides}\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\boxed{x=-(1)/(2)}\to\boxed{A)}`