Answer
$d=-1$
Work Step by Step
Given:$\dfrac{d}{d+2}-\dfrac{2}{2-d}=\frac{d+6}{d^2-4}$
As we know $a^2-b^2=(a-b)(a+b)$
$\dfrac{d}{d+2}-\dfrac{2}{2-d}=\frac{d+6}{(d-2)(d+2)}$
Need to find least common denominator(LCD).
$\dfrac{d}{d+2}+\dfrac{2}{d-2}=\dfrac{d+6}{(d-2)(d+2)}$
$d(d-2)+2)d+2)=d+6$
$d^2-d-2=0$
$(d+1)(d-2)=0$
Since, $d=2$ does not satisfy the given expression.Hence, the possible solution is $d=-1$
