Answer:
1/(x^2 +6x)
Step-by-step explanation:
The denominators used in your difference must have factors of x, (x-6), and (x +6). The only two tiles that have denominator factors on this list are the one you found, (x+2)/(x^2 -36), and the middle remaining one:
[tex]\dfrac{1}{x^2 +6x}=\dfrac{1}{x(x+6)}[/tex]
Your difference is ...
[tex]\dfrac{x+2}{x^2-36}-\dfrac{1}{x^2 +6x}=\dfrac{x^2+x+6}{x(x-6)(x+6)}[/tex]
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You can work out the sum on the left side to verify this.
[tex]\dfrac{x+2}{x^2-36}-\dfrac{1}{x^2 +6x}=\dfrac{x(x+2)-1(x-6)}{x(x-6)(x+6)}=\dfrac{x^2+2x-x+6}{x(x-6)(x+6)}[/tex]
Combining the two 'x' terms in the numerator of the last expression on the right gives the desired result.
