Solve frac{mu_{0}NI}{2l}(l/2-x/sqrt{(frac{D{2})^2+(l/2-x)^2}}+frac{l/2+2}{sqrt{(frac{D}{2})^2+(frac{l}{2}+x)^2}})

$$\frac { \mu _ { 0 } N I } { 2 l } ( \frac { \frac { l } { 2 } - x } { \sqrt { ( \frac { D } { 2 } ) ^ { 2 } + ( \frac { l } { 2 } - x ) ^ { 2 } } } + \frac { \frac { l } { 2 } + 2 } { \sqrt { ( \frac { D } { 2 } ) ^ { 2 } + ( \frac { l } { 2 } + x ) ^ { 2 } } } )$$

Evaluate

$$\frac{IN\mu _{0}\left(l\sqrt{4x^{2}+4lx+D^{2}+l^{2}}+l\sqrt{4x^{2}-4lx+D^{2}+l^{2}}-2x\sqrt{4x^{2}+4lx+D^{2}+l^{2}}+4\sqrt{4x^{2}-4lx+D^{2}+l^{2}}\right)}{2l\sqrt{-16\left(lx\right)^{2}+\left(4x^{2}+D^{2}+l^{2}\right)^{2}}}$$

$$l\neq 0\text{ and }\left(|l|\neq 2|x|\text{ or }D\neq 0\right)$$

Factor

$$\frac{\left(\frac{1}{\sqrt{4x^{2}+4lx+D^{2}+l^{2}}}+\frac{1}{\sqrt{4x^{2}-4lx+D^{2}+l^{2}}}-\frac{2x}{l\sqrt{4x^{2}-4lx+D^{2}+l^{2}}}+\frac{4}{l\sqrt{4x^{2}+4lx+D^{2}+l^{2}}}\right)IN\mu _{0}}{2}$$