Simplify frac a 2 - 100 8 div frac 2a 20 20 - SS2 Mathematics Algebraic Fractions Question
Simplify \(\frac{a^{2} - 100}{8} \div \frac{2a + 20}{20}\)
A
\(\frac{5(a - 10)}{4}\)
B
\(\frac{(a - 10)}{5}\)
C
\(\frac{5(a + 10)}{4}\)
D
\(\frac{2(2a - 5)}{10}\)
correct option: a
\[\frac{a^{2} - 100}{8} \div \frac{2a + 20}{20} = \ \frac{a^{2} - 100}{8} \times \frac{20}{2a + 20} = \frac{a^{2}{- 10}^{2}}{8} \times \frac{20}{2(a + 10)} = \ \frac{(a + 10)(a - 10)}{2} \times \frac{5}{2(a + 10)}\]
\(= \ \frac{a - 10}{2} \times \frac{5}{2} = \frac{5(a - 10)}{4}\)
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