Equation: ( 5 / (x-2) )=( 1 +(1/x) )
S smaxemow New member Joined May 18, 2008 Messages 3 May 18, 2008 #1 Equation: ( 5 / (x-2) )=( 1 +(1/x) )
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 May 18, 2008 #2 Re: Solving for x.. Please help Hello, smaxemow! \(\displaystyle \text{Solve: }\;\frac{5}{x-2} \:= \:1 + \frac{1}{x}\) Click to expand... \(\displaystyle \text{Muliply through by the LCD: }\:x(x-2)\) . . . \(\displaystyle x(x-2)\cdot\frac{5}{x-2} \;=\;x(x-2)\cdot 1 + x(x-2)\cdot\frac{1}{x}\) \(\displaystyle \text{and we have: }\;5x \;=\;x(x-2) + x-2 \quad\Rightarrow\quad x^2 - 6x - 2 \:=\:0\) \(\displaystyle \text{Quadratic Formula: }\;x \;=\;\frac{6 \pm\sqrt{44}}{2} \;=\;\boxed{3 \pm\sqrt{11}}\)
Re: Solving for x.. Please help Hello, smaxemow! \(\displaystyle \text{Solve: }\;\frac{5}{x-2} \:= \:1 + \frac{1}{x}\) Click to expand... \(\displaystyle \text{Muliply through by the LCD: }\:x(x-2)\) . . . \(\displaystyle x(x-2)\cdot\frac{5}{x-2} \;=\;x(x-2)\cdot 1 + x(x-2)\cdot\frac{1}{x}\) \(\displaystyle \text{and we have: }\;5x \;=\;x(x-2) + x-2 \quad\Rightarrow\quad x^2 - 6x - 2 \:=\:0\) \(\displaystyle \text{Quadratic Formula: }\;x \;=\;\frac{6 \pm\sqrt{44}}{2} \;=\;\boxed{3 \pm\sqrt{11}}\)
