To solve these algebraic expressions, we need to simplify each part step by step.

### Part (a)
$$\frac{21}{x-3} + \frac{9-6x}{x^2-3x}$$

First, factor the denominator of the second fraction:
$$x^2 - 3x = x(x-3)$$

So the expression becomes:
$$\frac{21}{x-3} + \frac{9-6x}{x(x-3)}$$

To combine these fractions, find a common denominator, which is $x(x-3)$:
$$\frac{21 \cdot x}{(x-3) \cdot x} + \frac{9-6x}{x(x-3)}$$
$$\frac{21x}{x(x-3)} + \frac{9-6x}{x(x-3)}$$

Combine the numerators:
$$\frac{21x + 9 - 6x}{x(x-3)}$$
$$\frac{15x + 9}{x(x-3)}$$

So, the simplified form of part (a) is:
$$\frac{15x + 9}{x(x-3)}$$

### Part (b)
$$\frac{4}{x+2} + \frac{2}{x-2} + \frac{5x-6}{x^2-4}$$

First, factor the denominator of the third fraction:
$$x^2 - 4 = (x+2)(x-2)$$

So the expression becomes:
$$\frac{4}{x+2} + \frac{2}{x-2} + \frac{5x-6}{(x+2)(x-2)}$$

To combine these fractions, find a common denominator, which is $(x+2)(x-2)$:
$$\frac{4 \cdot (x-2)}{(x+2)(x-2)} + \frac{2 \cdot (x+2)}{(x+2)(x-2)} + \frac{5x-6}{(x+2)(x-2)}$$
$$\frac{4(x-2) + 2(x+2) + 5x-6}{(x+2)(x-2)}$$

Simplify the numerator:
$$4(x-2) + 2(x+2) + 5x-6$$
$$4x - 8 + 2x + 4 + 5x - 6$$
$$(4x + 2x + 5x) + (-8 + 4 - 6)$$
$$11x - 10$$

So, the simplified form of part (b) is:
$$\frac{11x - 10}{(x+2)(x-2)}$$

Therefore, the simplified forms are:
(a) $$\frac{15x + 9}{x(x-3)}$$
(b) $$\frac{11x - 10}{(x+2)(x-2)}$$