6. $$ \frac{3}{4}+\left(\frac{1}{4}-\frac{1}{6}\right) $$

Question

UpStudy AI · Accepted Answer

To solve the expression:

$$
\frac{3}{4} + \left( \frac{1}{4} - \frac{1}{6} \right)
$$

**Step 1: Simplify the expression inside the parentheses**

$$
\frac{1}{4} - \frac{1}{6}
$$

To subtract these fractions, find a common denominator. The least common denominator (LCD) of 4 and 6 is 12.

$$
\frac{1}{4} = \frac{3}{12} \
\frac{1}{6} = \frac{2}{12}
$$

Now subtract:

$$
\frac{3}{12} - \frac{2}{12} = \frac{1}{12}
$$

**Step 2: Add the result to $$\frac{3}{4}$$**

$$
\frac{3}{4} + \frac{1}{12}
$$

Again, find a common denominator. The LCD of 4 and 12 is 12.

$$
\frac{3}{4} = \frac{9}{12} \
\frac{1}{12} = \frac{1}{12}
$$

Now add:

$$
\frac{9}{12} + \frac{1}{12} = \frac{10}{12}
$$

**Step 3: Simplify the final fraction**

$$
\frac{10}{12} = \frac{5}{6}
$$

**Final Answer:**

$$\boxed{\dfrac{5}{6}}$$
The final answer is $$\frac{5}{6}$$.

6. \( \frac{3}{4}+\left(\frac{1}{4}-\frac{1}{6}\right) \)