Solve the equation. Check the solution -4/x+1 = -1/x+5

 -4/x+1 = -1/x+5      cross  multiply

-4( x + 5)  = -1 ( x + 1)     simplify

-4x - 20  = -1x  - 1      add 1x, 20  to both sides

-3x = 19     divide both sides by -3

x  = -19 / 3

Check solution

-4/[ -19/3 + 1 ]  = -1 / [ -19/3 + 5]

-4/ [ -19/3 + 3/3]  = -1 / [ -19/3 + 15/3]

-4/ [ -16/3]  = -1 / [ -4/3]

-4*3 / -16  = -1 * 3 / -4

-12/ - 16  = -3 / -4

3/4  = 3/4