Question

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

Answer 1

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`and`3/x`would be`oo# Therefore #x=6#

Answer 2

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

`x = 6`

Explanation:

Given `1/2+2/x = 1/3+3/x`

Multiply both sides by `6x` to get:

`3x + 12 = 2x + 18`

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

`x = 6`