-7¾ - 4¼ ÷ (37-1)

$-7\frac{3}{4} = -\frac{(7 \times 4) + 3}{4} = -\frac{28+3}{4} = -\frac{31}{4}$
$4\frac{1}{4} = \frac{(4 \times 4) + 1}{4} = \frac{16+1}{4} = \frac{17}{4}$

$37 - 1 = 36$

$-\frac{31}{4} - \frac{17}{4} \div 36$

Dividing by a number is the same as multiplying by its reciprocal.
$\frac{17}{4} \div 36 = \frac{17}{4} \times \frac{1}{36} = \frac{17 \times 1}{4 \times 36} = \frac{17}{144}$

$-\frac{31}{4} - \frac{17}{144}$

The least common multiple of 4 and 144 is 144.
Convert $-\frac{31}{4}$ to a fraction with a denominator of 144.
$-\frac{31}{4} = -\frac{31 \times 36}{4 \times 36} = -\frac{1116}{144}$

$-\frac{1116}{144} - \frac{17}{144} = \frac{-1116 - 17}{144} = \frac{-1133}{144}$

$\frac{-1133}{144} = -7 \frac{1133 - (7 \times 144)}{144} = -7 \frac{1133 - 1008}{144} = -7 \frac{125}{144}$

The final answer is $-7\frac{125}{144}$.