How do you solve #\frac { 4} { x  3} + \frac { 3} { x + 9} = \frac { 6} { ( x + 9) ( x  3) }#?
1 Answer
But,
Explanation:
Let's start with the original problem:
Seeing as how there are fractions, we can multiply by both sides
Then we can use the Distributive Property to simplify out the left side:
Now we can cancel out some terms and then simplify the result:
We can use the Distributive Property again and simplify the equation:
We then combine like terms and move all the
We then divide both sides by
However, we're not done. We have to make sure that the value of our variable won't make any of the denominators in the original equation turn to
So, when
#x3=33=color(red)(6)# #x+9=3+9=color(red)6# #(x+9)(x3)=(3+9)(33)=(6)(6)=color(red)(36)#
None of these denominators are equal to
However, there are some solutions that do make the denominators

For the denominator
#x3# , if#color(blue)(x=3)# , then the denominator will turn to#0# , making#3# a value that#x# cannot be. 
For the denominator
#x+9# , if#color(blue)(x=9)# , then the denominator will turn to#0# , making#9# a value that#x# cannot be. 
For the denominator
#(x3)(x+9)# , if#color(blue)(x=3)# or#color(blue)(x=9)# , then the denominator will turn to#0# , making#3# and#9# values that#x# cannot be.
In conclusion,
Hope this helped!