Expand (a+b)(3+a/b): Multiplying Binomial Expressions Step-by-Step

To solve this problem, we'll use the distributive property, which states that for any numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.

Let's break it down step by step:

Step 1: Apply the distributive property
We will expand the expression $(a+b)(3+\frac{a}{b})$ by distributing the terms in $(a+b)$ over $(3+\frac{a}{b})$.

Step 2: Expand the expression
$(a+b)(3+\frac{a}{b})$ expands as follows:

• First, distribute $a$ to each term in $(3 + \frac{a}{b})$:
• $a \cdot 3 = 3a$
• $a \cdot \frac{a}{b} = \frac{a^2}{b}$
• Next, distribute $b$ to each term in $(3 + \frac{a}{b})$:
• $b \cdot 3 = 3b$
• $b \cdot \frac{a}{b} = a$ (because $b$ cancels with the denominator)

Step 3: Combine and simplify the results
Putting it all together, we have:

$3a + \frac{a^2}{b} + 3b + a$

Simplify the expression by combining like terms:

• $3a + a = 4a$

Thus, the simplified result is:

$4a + \frac{a^2}{b} + 3b$

Therefore, the solution to the problem is $4a + \frac{a^2}{b} + 3b$.