(3) $$ \frac{6 a^{4}+9 a^{4}}{5 a^{2}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{6 a^{4} + 9 a^{4}}{5 a^{2}}
$$

**Step 1: Combine Like Terms in the Numerator**

Both terms in the numerator have the same variable raised to the same power ($$a^4$$). You can add their coefficients directly.

$$
6 a^{4} + 9 a^{4} = (6 + 9) a^{4} = 15 a^{4}
$$

**Step 2: Rewrite the Expression with the Combined Numerator**

$$
\frac{15 a^{4}}{5 a^{2}}
$$

**Step 3: Simplify the Fraction**

- **Divide the coefficients:** $$ \frac{15}{5} = 3 $$
- **Subtract the exponents when dividing like bases:** $$ a^{4} \div a^{2} = a^{4-2} = a^{2} $$

$$
\frac{15 a^{4}}{5 a^{2}} = 3 a^{2}
$$

**Final Simplified Expression:**

$$
3 a^{2}
$$
The simplified expression is $$ 3a^{2} $$.

(3)