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

2 Answers
Dec 31, 2015

Answer:

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#

Dec 31, 2015

Answer:

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#