# How do you solve the rational equation 1 / 2 + 2 / x = 1 / 3 + 3 / x?

Dec 31, 2015

Get both sides onto a common denominator and simplify

#### Explanation:

(x +4)/(2x) = (x+9)/(3x)  => 3x(x+4)=2x(x+9) => 3x^2 +12x = 2x^2 +18x => 3x^2 - 2x^2 +12x - 18x = 0 => x^2 -6x = 0 => x(x-6) = 0 => x = 0 or x = 6 x!=0$\because$2/x$\mathmr{and}$3/x$w o \underline{d} b e$oo Therefore x=6#

Dec 31, 2015

Multiply through by $6 x$ then subtract $2 x + 12$ from both sides to find:

$x = 6$

#### Explanation:

Given $\frac{1}{2} + \frac{2}{x} = \frac{1}{3} + \frac{3}{x}$

Multiply both sides by $6 x$ to get:

$3 x + 12 = 2 x + 18$

Subtract $2 x + 12$ from both sides to get:

$x = 6$