Question 768328
 write the expression as a single logarithm using the addition and subtraction method
{{{log(x^2+2x-3)/(x^2-4)-log(x^2+7x+6)/(x+2) }}}
= {{{log((x^2+2x-3)/(x^2-4))/((x^2+7x+6)/(x+2)) }}}
Invert divisor and multiply
= {{{log((x^2+2x-3)/(x^2-4))*((x+2)/(x^2+7x+6))}}}
= {{{log((x^2+2x-3)/((x-2)*(x+2)))*((x+2)/(x^2+7x+6))}}}
Cancel x+2
= {{{log((x^2+2x-3)/((x-2)(x^2+7x+6)))}}}
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That's a single log, what was asked for.