![\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{(x+6)*(x+2)}{(x+7)*(x+2)}-\frac{(x+1)(x+7)}{(x+2)(x+7)}\\\\\\ =\frac{(x+6)*(x+2) - [(x+1)(x+7)]}{(x+2)(x+7)}\\\\\\= \frac{x^{2}+8x+12 -[x^{2}+8x+7]}{x^{2}+9x+14}\\\\\\=\frac{x^{2}+8x+12-x^{2}-8x-7}{x^{2}+9x+14}\\\\=\frac{5}{x^{2}+9x+14}\\\\\\\\\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{1}{3x+1}\\\\\frac{5}{x^{2}+9x+14}=\frac{1}{3x+1}\\\\](/tpl/images/1386/6181/06a5a.png)
Using quadratic equation
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