What is the solution set for #30/(x^2-9) - 5/(x-3) = 9/(x+3)#?

1 Answer
Aug 11, 2015

Answer:

I found no real solution!

Explanation:

You can write it as:
#30/((x+3)(x-3))-5/(x-3)=9/(x+3)#
the common denominator can be: #(x+3)(x-3)#; so you get:
#(30-5(x+3))/((x+3)(x-3))=(9(x-3))/((x+3)(x-3))#
#(30-5(x+3))/cancel(((x+3)(x-3)))=(9(x-3))/cancel(((x+3)(x-3)))#
#30-5x-15=9x-27#
collect #x# on the left:
#-14x=-42#
#x=42/14=3#
BUT substituting #x=3# into the original equation you get a division by zero!!! We have no real solutions.