Question

Simplify the expression. $$\frac{8}{2+3 x} \cdot(8+12 x)$$

Short answer

The simplified expression is \( \frac{96x + 64}{2+3x} \)

Step-by-step solution

Distribute the Multiplication

Firstly, distribute the fraction \( \frac{8}{2+3x} \) with each term in the parenthesis \( (8+12x) \). This results in: \( \frac{8}{2+3x} \cdot 8 + \frac{8}{2+3x} \cdot 12x \)

Simplify the Expressions

After doing the multiplication, simplify each fraction. The first becomes \( \frac{64}{2+3x} \) and the second one becomes \( \frac{96x}{2+3x}\)

Convert to Common Denominators

Both expressions have the same denominator \(2+3x\). This could be written as: \( \frac{64 + 96x}{2+3x} \)

Final Simplification

Rearrange the numerator to get the final simplified expression. The solution is: \( \frac{96x + 64}{2+3x} \)