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

##### 2 Answers
Jul 25, 2018

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

$4 x \times \frac{x}{4} - 4 x \times \frac{4}{x} = 4 x \times 0$

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

$x = \left(\frac{+}{-}\right) 4$

Jul 25, 2018

Add $\frac{4}{x}$ to both sides

$\implies \frac{x}{4} = \frac{4}{x}$

Cross multiply

${x}^{2} = 16$

Square root both sides

$x = \setminus \pm 4$