Question

I'm not sure how to proceed with where I am on simplifying a fraction. I am trying to simplify the fraction 1 / (y / 5 - 1).

Answer 1

We will simplify further as follows:

`\begin{gathered} (1)/((y)/(5)-1)=(1)/((y-5)/(5))=((1)(5))/((1)(y-5)) \\ \\ =(5)/(y-5) \end{gathered}`

***Sum of fractions***

`(a)/(b)+(c)/(d)=(ad+bc)/(bd)`

Now, using this with the information given we have:

`\begin{gathered} (y)/(5)-1=(y)/(5)-(1)/(1)=((y)(1)-(5)(1))/((5)(1)) \\ \\ =(y-5)/(5) \end{gathered}`

Now, we know that this expression was the denominator of 1, so:

`(1)/((y)/(5)-1)=(1)/((y-5)/(5))`

Now, using division of fractions

`((a)/(b))/((c)/(d))=((a)(d))/((b)(c))`

So, that is:

`((1)/(1))/((y-5)/(5))=((1)(5))/((1)(y-5))=(5)/(y-5)`