for the fractions in the equation $$ \frac{3}{x}+\frac{2}{5}=\frac{1}{15} $$

Question

UpStudy AI · Accepted Answer

To solve the equation involving fractions:

$$
\frac{3}{x} + \frac{2}{5} = \frac{1}{15}
$$

**Step 1: Isolate the Fraction with $$ x $$**

Subtract $$\frac{2}{5}$$ from both sides to isolate $$\frac{3}{x}$$:

$$
\frac{3}{x} = \frac{1}{15} - \frac{2}{5}
$$

**Step 2: Simplify the Right Side**

First, find a common denominator for the fractions on the right side. The least common denominator (LCD) of 15 and 5 is 15.

$$
\frac{1}{15} - \frac{2}{5} = \frac{1}{15} - \frac{6}{15} = \frac{1 - 6}{15} = \frac{-5}{15} = -\frac{1}{3}
$$

So, the equation becomes:

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

**Step 3: Solve for $$ x $$**

Cross-multiply to solve for $$ x $$:

$$
3 \times (-3) = 1 \times x
$$

$$
-9 = x
$$

**Solution:**

$$
x = -9
$$
$$ x = -9 $$

for the fractions in the equation