Question

Make r the subject - picture underneath

Answer 1

r =
`(6a)/(5m^2-1)`

Explanation:

Given

m =
`\sqrt{(6a+r)/(5r) }` ( square both sides )

m² =
`(6a+r)/(5r)` ( multiply both sides by 5r )

5rm² = 6a + r ( subtract r from both sides )

5rm² - r = 6a ← factor out r from each term on the left side

r(5m² - 1) = 6a ← divide both sides by (5m² - 1)

r =
`(6a)/(5m^2-1)`

Answer 2

The answer is r = 6a / (5m² - 1).

Explanation:

The steps are :

`m = \sqrt{ (6a + r)/(5r) }`

`{m}^(2) = (6a + r)/(5r)`

`5r {m}^(2) = 6a + r`

`5r {m}^(2) - r = 6a`

`r(5 {m}^(2) - 1) = 6a`

`r = \frac{6a}{5 {m}^(2) - 1 }`