Question

which represents the simplest form of $\frac{12x - 18}{4x^2 - 9} cdot \frac{2x^2 + 5x + 3}{3x + 3}$ (assuming that no denominator is zero)?1$\frac{2x - 3}{2x + 3}$$\frac{x + 1}{2x - 3}$3

Explanation:

Step1: Factor all numerators/denominators

• $12x-18=6(2x-3)$
• $4x^2-9=(2x-3)(2x+3)$
• $2x^2+5x+3=(2x+3)(x+1)$
• $3x+3=3(x+1)$

The expression becomes:
$$\frac{6(2x-3)}{(2x-3)(2x+3)} \cdot \frac{(2x+3)(x+1)}{3(x+1)}$$

Step2: Cancel common factors

Cancel $(2x-3)$, $(2x+3)$, $(x+1)$:
$$\frac{6}{1} \cdot \frac{1}{3}$$

Step3: Multiply remaining terms

$$\frac{6}{3}=2$$

Answer:

2