## Elementary Algebra

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