The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{28\sqrt{40}}{4\sqrt{8}} \)
\( \frac{28}{4} \) \( \sqrt{\frac{40}{8}} \)
7 \( \sqrt{5} \)

To simplify a radical, factor out the perfect squares:

\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)

The number of students taking German or Spanish is 13 + 12 = 25. Of that group of 25, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 25 - 5 = 20 who are taking at least one language. 34 - 20 = 14 students who are not taking either language.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{4!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{5}{1} \)
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