[tex]\frac{5}{8}x+\frac{1}{16}x=\frac{5}{16+x}[/tex]
[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}8,\:16,\:16+x:\quad 16\left(x+16\right)[/tex]
[tex]\mathrm{Multiply\:by\:LCM=}16\left(x+16\right), \frac{5}{8}x\cdot \:16\left(x+16\right)+\frac{1}{16}x\cdot \:16\left(x+16\right)=\frac{5}{16+x}\cdot \:16\left(x+16\right)[/tex]
[tex]Simplify, 11x\left(x+16\right)=80[/tex]
[tex]\mathrm{Solve\:}\:11x\left(x+16\right)=80:\quad x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}[/tex]
[tex]x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}[/tex]
[tex]\mathrm{Verifying\:Solutions}[/tex]
[tex]Solution, x=\frac{4\left(7\sqrt{11}-22\right)}{11},\:x=-\frac{4\left(22+7\sqrt{11}\right)}{11}[/tex]
