Answer: C) [tex]r=a(\dfrac{S-1}{S})[/tex]
Step-by-step explanation:
The given formula : [tex]S=\dfrac{a}{(a-r)}[/tex]
To rearrange the formula to find the formula for r , first we multiply both sides with (a-r), we get
[tex](a-r)S=a[/tex]
Divide both sides by S , we get
[tex]a-r=\dfrac{a}{S}[/tex]
Subtract a on both sides , we get
[tex]-r=\dfrac{a}{S}-a\\\\ -r=a(\dfrac{1}{S}-1)[/tex]
Multiplying (-1) on both sides , we get
[tex]r=-a(\dfrac{1}{S}-1)\\\\ r=a(1-\dfrac{1}{S})\\\\ r=a(\dfrac{S-1}{S})[/tex]
Hence, the correct answer is : C) [tex]r=a(\dfrac{S-1}{S})[/tex]
