Questions: Simplify (1/(30 x) + 1/15) / (1/3 + 1/(6 x)) 1/5 1/(6 x) 5 1/(5 x) I don't know.

Solution Steps

We start with the numerator of the expression:

$$\frac{1}{30 x} + \frac{1}{15}$$

To combine these fractions, we find a common denominator, which is $30x$:

$$\frac{1}{30 x} + \frac{2x}{30 x} = \frac{1 + 2x}{30x}$$

Next, we simplify the denominator:

$$\frac{1}{3} + \frac{1}{6 x}$$

The common denominator here is $6x$:

$$\frac{2x}{6x} + \frac{1}{6x} = \frac{2x + 1}{6x}$$

Now we can rewrite the original expression as:

$$\frac{\frac{1 + 2x}{30x}}{\frac{2x + 1}{6x}}$$

This can be simplified by multiplying by the reciprocal of the denominator:

$$\frac{1 + 2x}{30x} \cdot \frac{6x}{2x + 1}$$

Now we simplify the expression:

Factoring gives us:

• Numerator: $6x(2x + 1)$
• Denominator: $30x(2x + 1)$

Thus, the expression simplifies to:

$$\frac{6x(2x + 1)}{30x(2x + 1)} = \frac{6}{30} = \frac{1}{5}$$

Final Answer