Write the expression as a simplified rational expression. (5)/((1)/(6) +(1)/(x+1) )

Question

Write the expression as a simplified rational expression.


`(5)/((1)/(6) +(1)/(x+1) )`

Answer 1

`\bf \cfrac{5}{(1)/(6)+(1)/(x+1)}\implies \cfrac{5}{\stackrel{\textit{our LCD here will just be 6(x+1)}}{((x+1)1~~+~~(6)1)/(6(x+1))}}\implies \cfrac{5}{(x+1~~+~~6)/(6(x+1))} \\\\\\ \cfrac{(5)/(1)}{~~(x+7)/(6(x+1))~~}\implies \cfrac{5}{1}\cdot \cfrac{6(x+1)}{x+7}\implies \cfrac{30(x+1)}{x+7}`

now, we could distribute the 30 up there, but simplification wise, it won't matter.