Hi, Can someone please show me how this problem is solved:

Here is one of my attempts:

First, I found LCD, so I can subtract the two expressions. I did so by multiplying (m-6) to (m^2-36) and (m^2-36) to (m-6) in the denominators. I also multiplied the numerators of each fraction by the same binomial their denominators were multiplied by in order to get to the LCD.

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Second, I simplified each numerator and combined the two expressions into one, with the LCD as the denominator.

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Third, I simplified the numerator of the expression.

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However, this is not the solution. The correct answer is actually:

Can someone please explain to me how to solve this problem?