How do you solve #\frac { 7} { x + 6} + \frac { 5} { x - 6} = \frac { 6} { ( x + 6) ( x - 6) }#?

2 Answers
May 21, 2017

Answer:

#x=3/2#

#3# is the numerator and #2# is the denominator.

Explanation:

Let's solve your equation step-by-step.

Multiply all terms to get #(x+6)(x-6)# as the denominators and cancel:

#7(x−6)+5(x+6)=6#

#12x−12=6" "#(Simplify both sides of the equation)

#12x−12+12=6+12" "#(Add #12# to both sides)

#12x=18#

#(12x)/12=18/12" "#(Divide both sides by #12#)

#x=3/2#

Check the answer. (Plug it in to make sure it works)

#x=3/2" "#(Works in original equation)

Answer:

#x=3/2#

(#3# is the numerator and #2# is the denominator)

May 21, 2017

Answer:

#x=3/2#

Explanation:

First, rule out the solutions #x=6# and #x=-6# since they will result in indeterminate forms (dividing by 0).

Now, multiply both sides by #(x+6)(x-6)#

#7(x-6)+5(x+6)=6 " "x !in{-6,6}#

From here, distribute and solve normally, keeping in mind the extraneous solutions -6 and 6.

#7x-42+5x+30=6 color(white)"XXXXX" x!in{-6,6}#
#color(white)"XXX/XX"12x-12=6 color(white)"XXXXX"x!in{-6,6}#
#color(white)"XXXXXXXX.." 12x=18 color(white)"XXXX."x!in{-6,6}#
#color(white)"XXXXXXXXXX" x=3/2#

Final Answer