The expression shown in the image is:

$\frac{\frac{1}{2} + \frac{b}{4}}{\frac{1}{2} + \frac{b}{3}}$

To simplify this expression, follow these steps:

1. Simplify the Numerator and Denominator:

• Numerator: $\frac{1}{2} + \frac{b}{4}$

  • Find a common denominator for the terms. The common denominator for $2$ and $4$ is $4$.
  • Rewrite $\frac{1}{2}$ as $\frac{2}{4}$.
  • So, the numerator becomes $\frac{2}{4} + \frac{b}{4} = \frac{2 + b}{4}$.

• Denominator: $\frac{1}{2} + \frac{b}{3}$

  • Find a common denominator for the terms. The common denominator for $2$ and $3$ is $6$.
  • Rewrite $\frac{1}{2}$ as $\frac{3}{6}$ and $\frac{b}{3}$ as $\frac{2b}{6}$.
  • So, the denominator becomes $\frac{3}{6} + \frac{2b}{6} = \frac{3 + 2b}{6}$.

2. Substitute Back:

Now the expression becomes:

$\frac{\frac{2 + b}{4}}{\frac{3 + 2b}{6}}$

3. Simplify the Fraction:

To simplify this complex fraction, multiply by the reciprocal of the denominator:

$\frac{2 + b}{4} \times \frac{6}{3 + 2b} = \frac{(2 + b) \times 6}{4 \times (3 + 2b)} = \frac{6(2 + b)}{4(3 + 2b)}$

4. Simplify Further:

Simplify the coefficients:

$\frac{6(2 + b)}{4(3 + 2b)} = \frac{3(2 + b)}{2(3 + 2b)}$

This is the simplified form of the expression.

Would you like any further details or have any questions?

Here are some related questions you might find helpful:

1. How do you simplify complex fractions in general?
2. What are the rules for finding a common denominator?
3. How do you multiply and divide fractions?
4. Can this expression be simplified further under certain conditions?
5. What happens if $b = 0$ in this expression?

Tip: When simplifying fractions, always look for opportunities to factor and cancel common terms to achieve the simplest form.