Question 142983
{{{3/(8x+1)+8/(2x+5)=1}}} Start with the given equation




{{{(8x+1)(2x+5)(3/cross(8x+1)+8/cross(2x+5))=1}}} Multiply both sides by the LCD {{{(8x+1)(2x+5)}}}



{{{3(2x+5)+8(8x+1)=(8x+1)(2x+5)}}} Distribute



{{{6x+15+64x+8=(8x+1)(2x+5)}}} Distribute again



{{{6x+15+64x+8=16x^2+42x+5}}} Foil



{{{6x+15+64x+8-16x^2-42x-5=0}}}  Subtract 16x^2 from both sides.  Subtract 42x from both sides.  Subtract 5 from both sides. 



{{{-16x^2+28x+18=0}}}  Combine like terms




{{{-2(4x-9)(2x+1)=0}}} Factor the left side 




Now set each factor equal to zero:

{{{4x-9=0}}} or  {{{2x+1=0}}} 


{{{x=9/4}}} or  {{{x=-1/2}}}    Now solve for x in each case



So our answers are


 {{{x=9/4}}} or  {{{x=-1/2}}}