5) $$ \frac{4 a-5}{6 a^{2}+30 a}+\frac{a-1}{6 a^{2}+30 a} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{4a - 5}{6a^{2} + 30a} + \frac{a - 1}{6a^{2} + 30a}
$$

**Step 1: Combine the Fractions**

Both fractions have the same denominator, so you can combine the numerators directly:

$$
\frac{4a - 5 + a - 1}{6a^{2} + 30a} = \frac{5a - 6}{6a^{2} + 30a}
$$

**Step 2: Factor the Denominator**

Factor out the greatest common factor (GCF) from the denominator:

$$
6a^{2} + 30a = 6a(a + 5)
$$

**Step 3: Rewrite the Expression with Factored Denominator**

$$
\frac{5a - 6}{6a(a + 5)}
$$

**Final Simplified Form:**

$$
\boxed{\dfrac{5a - 6}{6a(a + 5)}}
$$

This is the simplified form of the given expression.
$$ \frac{5a - 6}{6a(a + 5)} $$

Upstudy AI Solution