2) Упростите выражение a) 3x x-3 + x+5 6-2x + 54 5x+x² ; б) 48x 16-x² : ( x+4 x-4 - x-4 x+4 ).

2) Упростите выражение

a) $$\frac{3x}{x-3} + \frac{x+5}{6-2x} + \frac{54}{5x+x^2} = \frac{3x}{x-3} - \frac{x+5}{2(x-3)} + \frac{54}{x(5+x)} = \frac{6x \cdot x - x(x+5) \cdot x + 54 \cdot 2(x-3)}{2x(x-3)(x+5)} =$$ $$\frac{6x^2 - x(x^2+5x) + 108(x-3)}{2x(x-3)(x+5)} = \frac{6x^2 - x^3 - 5x^2 + 108x - 324}{2x(x-3)(x+5)} = \frac{-x^3 + x^2 + 108x - 324}{2x(x-3)(x+5)}$$

Ответ: $$\frac{-x^3 + x^2 + 108x - 324}{2x(x-3)(x+5)}$$

б) $$\frac{48x}{16-x^2} : (\frac{x+4}{x-4} - \frac{x-4}{x+4}) = \frac{48x}{(4-x)(4+x)} : (\frac{(x+4)^2-(x-4)^2}{(x-4)(x+4)}) = \frac{48x}{(4-x)(4+x)} : (\frac{x^2+8x+16 - (x^2-8x+16)}{(x-4)(x+4)}) = $$ $$\frac{48x}{(4-x)(4+x)} : (\frac{x^2+8x+16 - x^2+8x-16}{(x-4)(x+4)}) = \frac{48x}{(4-x)(4+x)} : (\frac{16x}{(x-4)(x+4)}) = \frac{48x}{(4-x)(4+x)} \cdot \frac{(x-4)(x+4)}{16x} =$$ $$\frac{48x}{-(x-4)(4+x)} \cdot \frac{(x-4)(x+4)}{16x} = \frac{48x \cdot (x-4)(x+4)}{-16x \cdot (x-4)(x+4)} = -3$$

Ответ: $$-3$$