Question

Subtract. please help
`\frac{1}{3 {x}^(2) } - \frac{x}{ {x}^(2) - 8}`

Answer 1

`(1)/(3x^2)-(x)/(x^2-8)`

Find the LCM and subtarct the numerator

`\text{LCM }=3x^2(x^2-8)\text{ }`

`\begin{gathered} =(\left(x+2√(2)\right)\left(x-2√(2)\right))/(3x^2\left(x+2√(2)\right)\left(x-2√(2)\right))-(3x^3)/(3x^2\left(x+2√(2)\right)\left(x-2√(2)\right)) \\ \mathrm{Apply\: the\: fraction\: rule}\colon\quad (a)/(c)-(b)/(c)=(a-b)/(c) \end{gathered}`
`\begin{gathered} =(\left(x+2√(2)\right)\left(x-2√(2)\right)-3x^3)/(3x^2\left(x+2√(2)\right)\left(x-2√(2)\right)) \\ =(x^2-8-3x^3)/(3x^2\left(x+2√(2)\right)\left(x-2√(2)\right)) \end{gathered}`
`\begin{gathered} Expand(x+2\sqrt[]{2)}(x-2\sqrt[]{2)} \\ =(x^2-8-3x^3)/(3x^2\left(x^2-8\right)) \end{gathered}`