Answer
$x=${$\dfrac{5 - \sqrt {73}}{2},\dfrac{5 + \sqrt {73}}{2}$}
Work Step by Step
Given: $\dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{1}{4}$
Re-write the given equation as: $x^2-5x-12=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-5) \pm \sqrt{(-5)^2-4(1)(-12)}}{2(1)}$
or, $x=\dfrac{5 \pm \sqrt {73}}{2}$
Hence, our solution set is: $x=${$\dfrac{5 - \sqrt {73}}{2},\dfrac{5 + \sqrt {73}}{2}$}
