9) $$ \frac{16}{\frac{x}{25}-\frac{4}{25}} $$

Question

UpStudy AI · Accepted Answer

1. Write the original expression:
   $$
   \frac{16}{\frac{x}{25}-\frac{4}{25}}
   $$

2. Combine the fractions in the denominator:
   $$
   \frac{x}{25}-\frac{4}{25}=\frac{x-4}{25}
   $$

3. Substitute back into the expression:
   $$
   \frac{16}{\frac{x-4}{25}}
   $$

4. Use the rule of dividing by a fraction (multiplying by its reciprocal):
   $$
   \frac{16}{\frac{x-4}{25}} = 16\cdot\frac{25}{x-4}
   $$

5. Multiply the numerator:
   $$
   16\cdot25=\ 400
   $$

6. Write the final expression:
   $$
   \frac{400}{x-4}
   $$
The simplified expression is $$ \frac{400}{x-4} $$.

Upstudy AI Solution