Simplify DONE $$ \frac{\frac{16 m^{2}}{m^{2}+5}}{3 m^{2}+15} $$ DOS

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UpStudy AI · Accepted Answer

1. Start with the given expression:
   $$
   \frac{\frac{16 m^{2}}{m^{2}+5}}{3 m^{2}+15}
   $$

2. Interpret the division as multiplication by the reciprocal:
   $$
   \frac{16 m^{2}}{m^{2}+5} \cdot \frac{1}{3 m^{2}+15}
   $$

3. Factor the denominator $$3 m^{2}+15$$:
   $$
   3 m^{2}+15 = 3(m^{2}+5)
   $$
   Hence, the expression becomes:
   $$
   \frac{16 m^{2}}{m^{2}+5} \cdot \frac{1}{3(m^{2}+5)}
   $$

4. Multiply the numerators and denominators:
   $$
   \frac{16 m^{2}}{3(m^{2}+5)(m^{2}+5)} = \frac{16 m^{2}}{3 (m^{2}+5)^2}
   $$

5. The simplified expression is:
   $$
   \frac{16 m^{2}}{3 (m^{2}+5)^2}
   $$
The simplified expression is $$ \frac{16 m^{2}}{3 (m^{2}+5)^2} $$.

Simplify DONE \( \frac{\frac{16 m^{2}}{m^{2}+5}}{3 m^{2}+15} \) DOS

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