(b) $$ \frac{3}{p}+\frac{5}{2 p}-\frac{2}{p^{2}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{3}{p} + \frac{5}{2p} - \frac{2}{p^{2}}
$$

**Step 1: Combine Like Terms**

First, combine the terms that have the same denominator:

$$
\frac{3}{p} + \frac{5}{2p} = \frac{6}{2p} + \frac{5}{2p} = \frac{11}{2p}
$$

**Step 2: Combine All Terms Over a Common Denominator**

Now, combine the result with the remaining term:

$$
\frac{11}{2p} - \frac{2}{p^{2}}
$$

To combine these, find a common denominator, which is $$2p^{2}$$:

$$
\frac{11}{2p} = \frac{11p}{2p^{2}}
$$
$$
\frac{2}{p^{2}} = \frac{4}{2p^{2}} \quad (\text{since } \frac{2}{p^{2}} = \frac{4}{2p^{2}})
$$

Now, subtract the fractions:

$$
\frac{11p}{2p^{2}} - \frac{4}{2p^{2}} = \frac{11p - 4}{2p^{2}}
$$

**Final Simplified Expression:**

$$
\frac{11p - 4}{2p^{2}}
$$
The simplified expression is $$ \frac{11p - 4}{2p^{2}} $$.

(b) \( \frac{3}{p}+\frac{5}{2 p}-\frac{2}{p^{2}} \)