Question

Solve. Find exact solution: (3/x+5)-(11/3x-1)=-1

Answer 1

is it
\[\frac{3}{x+5}-\frac{11}{3x-1}=-1\]?

Answer 2

yes

Answer 3

these are a pain in the neck
multiply both sides by
\[(x+5)(3x-1)\] to get
\[3(3x-1)-11(x+5)=-(x+5)(3x-1)\] as a first step

Answer 4

then multiply out and get
\[9x-3-11x-55=-3 x^2-14 x+5\] and go from there

Answer 5

ok :)
whats next

Answer 6

combine like terms
set it equal to zero, solve the resulting quadratic equation

Answer 7

if you do that correctly, you should get \[3 x^2+12 x-63 = 0\]

Answer 8

divide by 3 and get
\[x^2+4x-21=0\] which fortunately for your factors as
\[(x+7)(x-3)=0\]