5. Выполните действия с рациональными дробями: 1) 3x/(4+x)+(16+x)/(4+x); 2) 3x/(x−4)−(x+8)/(x−4); 3) 9/(x+1)+9x/(x+1); 4) 16/(x+2)+8x/(x+2); 5) 4x/(x+1)−(x−3)/(x+1); 6) (y−x)/(y²−9)−(3−x)/(y²−9); 7) (x+y)/(4−x²)−(y−2)/(4−x²); 8) (2x+17)/(49−x²)−(10+x)/(49−x²); 9) (y²+30)/(y−6)−(6−12y)/(6−y); 10) (y²−8y)/(y−3)−(9+2y)/(3−y).

1. \(\dfrac{3x}{x+4}+\dfrac{x+16}{x+4}=\dfrac{4x+16}{x+4}=\dfrac{4(x+4)}{x+4}=4\), \(x\ne-4\).
2. \(\dfrac{3x}{x-4}-\dfrac{x+8}{x-4}=\dfrac{3x-x-8}{x-4}=\dfrac{2(x-4)}{x-4}=2\), \(x\ne4\).
3. \(\dfrac{9}{x+1}+\dfrac{9x}{x+1}=\dfrac{9+9x}{x+1}=\dfrac{9(x+1)}{x+1}=9\), \(x\ne-1\).
4. \(\dfrac{16}{x+2}+\dfrac{8x}{x+2}=\dfrac{16+8x}{x+2}=\dfrac{8(x+2)}{x+2}=8\), \(x\ne-2\).
5. \(\dfrac{4x}{x+1}-\dfrac{x-3}{x+1}=\dfrac{4x-x+3}{x+1}=\dfrac{3(x+1)}{x+1}=3\), \(x\ne-1\).
6. \(\dfrac{y-x}{y^2-9}-\dfrac{3-x}{y^2-9}=\dfrac{y-3}{(y-3)(y+3)}=\dfrac{1}{y+3}\), \(y\ne-3,3\).
7. \(\dfrac{x+y}{4-x^2}-\dfrac{y-2}{4-x^2}=\dfrac{x+2}{(2-x)(2+x)}=\dfrac{1}{2-x}\), \(x\ne-2,2\).
8. \(\dfrac{2x+17}{49-x^2}-\dfrac{x+10}{49-x^2}=\dfrac{x+7}{(7-x)(7+x)}=\dfrac{1}{7-x}\), \(x\ne-7,7\).
9. \(\dfrac{y^2+30}{y-6}-\dfrac{6-12y}{6-y}=\dfrac{y^2+30-(12y-6)}{y-6}=\dfrac{(y-6)^2}{y-6}=y-6\), \(y\ne6\).
10. \(\dfrac{y^2-8y}{y-3}-\dfrac{9+2y}{3-y}=\dfrac{y^2-8y+9+2y}{y-3}=\dfrac{(y-3)^2}{y-3}=y-3\), \(y\ne3\).

Ответ: 1) 4; 2) 2; 3) 9; 4) 8; 5) 3; 6) \(\dfrac{1}{y+3}\); 7) \(\dfrac{1}{2-x}\); 8) \(\dfrac{1}{7-x}\); 9) \(y-6\); 10) \(y-3\).