Problem
Seven divided by the difference of a number and 2 , minus 6 divided by a number plus 2 , equals 6 times the reciprocal of the difference of the number squared and 4 . What is the number?
Solution
Step 1 ：\[ \frac{7}{x-2} - \frac{6}{x+2} = 6\left(\frac{1}{x^2 - 4}\right) \]
Step 2 ：\[ (x^2 - 4)\left(\frac{7}{x-2} - \frac{6}{x+2}\right) = 6 \]
Step 3 ：\[ x = 4 , x = -4 \]
