Question

How do you solve `x/4 - 4/x=0`?

Answer 1

Work backwards combine like terms and remove the fractions

Explanation:

The order of operations is PEMDAS in reverse it is PESADM

Start by removing the parenthesis a / divided symbol acts as a parenthesis so remove the division symbols like this

`4x xx (x)/4 - 4x xx (4)/x = 4x xx 0`

Dividing out the common terms gives

`x^2 - 16 = 0`

Work backwards by subtracting 16 from both sides

`x^2 - 16 +16 = 0 +16`

This gives

`x^2 = 16`

Taking the square root of both sides gives

`sqrt x^2 = sqrt 16`

Which gives and imaginary number

`x = (+/- )4`

Answer 2

Add `4/x` to both sides

`=> x/4=4/x`

Cross multiply

`x^2=16`

Square root both sides

`x= \pm4`