How do you solve #1/(x+3) + 1/(x-3) = 1/(x^2-9)#?

1 Answer
Feb 28, 2016

Answer:

The only configuration that yields a logical answer is:
#1/(x+3)+1/(x-3) = 1/(x^2-9)#

In which case#" "x=1/2#

Explanation:

Considering different configuration:

#color(blue)("Configuration 1")#
Suppose the Left hand side was meant to be #" "1/(x+3)+1/(x-3)#

Then the left would be:

#((x+3)+(x-3))/(x^2-9)#

Comparing left to right gives

#x+3+x-3=1#

#2x=1#

#x=1/2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Configuration 2")#

Suppose the Left hand side was meant to be #" "1/(x+3)-1/(x-3)#

Then the left would be:

#((x+3)-(x-3))/(x^2-9)= 6/(x^2-9)#

Comparing Left to right would mean that it would have to be true for

#6=1" "color(red)("Clearly this is a contradiction so it is not the case")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("The only possible scenario is for configuration 1")#

#color(magenta)("So the answer is "x=1/2)#