Answer
$-\frac{1}{2}$
Work Step by Step
Use the order of operations to simplify the expression:$$\frac{(5-6)^{2}-2|3-7|}{89-3\times5^{2}}$$
As the fraction itself defines grouping symbols, the numerator and denominator are each individual groups. Within each group start with Grouped operations. Remember, absolute value bars are gouping symbols as well as parentheses.$$=\frac{(-1)^{2}-2|-4|}{89-3\times5^{2}}$$
The absolute value is the distance of that number to zero. Negative 4 is four spaces away from zero, so the absolute value of -4 is 4:$$=\frac{(-1)^{2}-2(4)}{89-3\times5^{2}}$$
Next complete any exponents, then multiplication and division in order left to right, and finally addition and subtraction left to right:$$=\frac{1-2(4)}{89-3\times25}$$ $$=\frac{1-8}{89-75}$$ $$=\frac{(-7)}{14}$$
Finish with the division implied by the fraction or reduce the fraction: $$=-\frac{1}{2}$$
