fractions in the equation $$ \frac{3}{5 x}-\frac{1}{x}=\frac{6}{15} $$

Question

UpStudy AI · Accepted Answer

To solve the equation involving fractions:

$$
\frac{3}{5x} - \frac{1}{x} = \frac{6}{15}
$$

Let's follow the step-by-step process to find the value of $$ x $$.

### Step 1: Simplify the Equation

First, simplify the right-hand side of the equation:

$$
\frac{6}{15} = \frac{2}{5}
$$

So, the equation becomes:

$$
\frac{3}{5x} - \frac{1}{x} = \frac{2}{5}
$$

### Step 2: Find a Common Denominator

The denominators in the equation are $$ 5x $$ and $$ x $$. The least common denominator (LCD) for these fractions is $$ 5x $$.

### Step 3: Eliminate the Fractions

Multiply every term in the equation by the LCD ($$ 5x $$) to eliminate the fractions:

$$
5x \cdot \frac{3}{5x} - 5x \cdot \frac{1}{x} = 5x \cdot \frac{2}{5}
$$

### Step 4: Simplify Each Term

Simplify each term after multiplication:

1. $$ 5x \cdot \frac{3}{5x} = 3 $$
2. $$ 5x \cdot \frac{1}{x} = 5 $$
3. $$ 5x \cdot \frac{2}{5} = 2x $$

So, the equation now is:

$$
3 - 5 = 2x
$$

### Step 5: Solve for $$ x $$

Combine like terms:

$$
-2 = 2x
$$

Now, divide both sides by 2 to isolate $$ x $$:

$$
x = \frac{-2}{2} = -1
$$

### Conclusion

The solution to the equation is:

$$
x = -1
$$
$$ x = -1 $$

fractions in the equation \( \frac{3}{5 x}-\frac{1}{x}=\frac{6}{15} \)