Simplify $$ \frac{\frac{3}{x^{2}}}{\frac{5}{x}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\frac{3}{x^{2}}}{\frac{5}{x}}
$$

follow these steps:

1. **Rewrite the Division as Multiplication:**

Dividing by a fraction is the same as multiplying by its reciprocal. So,

$$
   \frac{\frac{3}{x^{2}}}{\frac{5}{x}} = \frac{3}{x^{2}} \times \frac{x}{5}
   $$

2. **Multiply the Numerators and the Denominators:**

$$
   \frac{3 \times x}{x^{2} \times 5} = \frac{3x}{5x^{2}}
   $$

3. **Simplify the Expression:**

You can cancel one $$ x $$ from the numerator and the denominator:

$$
   \frac{3x}{5x^{2}} = \frac{3}{5x}
   $$

*(Here, $$ x \neq 0 $$ to avoid division by zero.)*

So, the simplified form of the original expression is:

$$
\frac{3}{5x}
$$
The simplified form is $$ \frac{3}{5x} $$.

Simplify \( \frac{\frac{3}{x^{2}}}{\frac{5}{x}} \)