Question

How do you solve this? My algebra 2 teacher taught it to us in class but it still confuses me! Thank you!

Answer 1

`\bf \cfrac{(1)/(8)-(1)/(2x)}{(1)/(12x)-(1)/(3x^2)} \begin{array}{llll} \leftarrow \textit{our LCD here will just be }8x\\[0.9em] \leftarrow \textit{our LCD down here will be }12x^2 \end{array}`

`\bf \cfrac{~~((x)1-(4)1)/(8x)~~}{((x)1-(4)1)/(12x^2)}\implies \cfrac{~~(x-4)/(8x)~~}{(x-4)/(12x^2)}\implies \cfrac{~~\begin{matrix} x-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{\underset{2}{~~\begin{matrix} 8x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{3x}{~~\begin{matrix} 12x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} x-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{3x}{2}`