#### Answer

{$-\frac{23}{5}$}

#### Work Step by Step

Through cross multiplication, we will eliminate the fractional form of the equation. Then, we simplify:
$\frac{4}{x-1}=\frac{-1}{x+6}$
$4(x+6)=-1(x-1)$
$4x+24=-x+1$
$4x+x=1-24$
$5x=-23$
$x=-\frac{23}{5}$
Therefore, the solution set is {$-\frac{23}{5}$}.