Question

How do you solve `a-5/a=4`?

Answer 1

`a = 5`

Explanation:

`a-5/a=4`

multiply by `a`:

`a^2 - 5 = 4a`

add `5`:

`a^2 = 4a + 5`

`a^2>4a`

`a>4`

trial:
`a = 5`

`a^2 = 4a+5`

`= 20+5 = 25`

`a^2 = 25`

`a = 5`

Answer 2

`a= 5 " or "a =-1`

Explanation:

`a -5/a = 4" "larr` we can see `a !=0`

Multiply by `a` to get rid of the fraction.

`a^2 -5 =4a" "larr` a quadratic, make it equal to 0

`a^2 -4a -5 =0" "larr` factorise

`(a-5)(a+1)= 0" "larr` either factor can be =0

If `a-5 = 0, " then " a = 5`

If `a +1 = 0, " then " a =-1`