Simplify algebraic fractions by multiplication or division

1. Express

$$\frac { 2 x ^ { 3 } + x ^ { 2 } } { x ^ { 2 } - 4 } \times \frac { x - 2 } { 2 x ^ { 2 } - 5 x - 3 }$$ as a single fraction in its simplest form.

Factorise and hence simplify the following expression. $$\frac{x^2 - 9}{x^2 + 5x + 6}$$ [3]

Express as a single fraction in its simplest form $$\frac{x^2 - 8x + 15}{x^2 - 9} \times \frac{2x^2 + 6x}{(x - 5)^2}$$ [4]

Simplify fully $$\frac{(x + 3)(6 - 2x)}{(x - 3)(3 + x)} \quad \text{for } x \neq \pm 3$$ Circle your answer. [1 mark] \(-2\) \quad \(2\) \quad \(\frac{(6 - 2x)}{(x - 3)}\) \quad \(\frac{(2x - 6)}{(x - 3)}\)