99. Представьте в виде дроби и, если возможно, упростите выражение: 1) 9/(n² − 9n) + 1/(9 − n); 2) 4/(n + 7) + 4n/(7n + 49); 3) 1/(a² − 5a) + 1/(25 − 5a); 4) 1/(x² − 3x) + 1/(9 − 3x); 5) 1/(y² + 5y) + 1/(25 + 5y); 6) 1/(16 − 4c) + 1/(c² − 4c); 7) (16a − 15)/(3a² − 2a) − 13/(4 − 6a); 8) 11/(2x − 5) + (9x + 5)/(5x − 2x²); 9) 9b/(2a² − 3ab) − 4a/(2ab − 3b²); 10) 4x/(5y² − 2xy) − 25y/(5xy − 2x²); 11) 3/(a² + 4ac) − 6/(a² − 16c²); 12) 12/(9a² − 16b²) − 2/(3a² − 4ab); 13) 1/(a² − x²) + 1/(2ax + 2x²); 14) 4/(c² − 4p²) − 1/(cp − 2p²); 15) 1/(10xy + 50y²) + 1/(x² − 25y²); 16) 1/(12ac − 8c²) − 1/(4c² − 9a²).

1. \(\frac{9}{n(n-9)}-\frac{1}{n-9}=\frac{9-n}{n(n-9)}=-\frac1n\).
2. \(\frac4{n+7}+\frac{4n}{7(n+7)}=\frac{28+4n}{7(n+7)}=\frac47\).
3. \(\frac1{a(a-5)}-\frac1{5(a-5)}=\frac{5-a}{5a(a-5)}=-\frac1{5a}\).
4. \(\frac1{x(x-3)}-\frac1{3(x-3)}=\frac{3-x}{3x(x-3)}=-\frac1{3x}\).
5. \(\frac1{y(y+5)}+\frac1{5(y+5)}=\frac{y+5}{5y(y+5)}=\frac1{5y}\).
6. \(\frac1{4(4-c)}+\frac1{c(c-4)}=-\frac1{4(c-4)}+\frac1{c(c-4)}=-\frac1{4c}\).
7. \(\frac{16a-15}{a(3a-2)}+\frac{13}{2(3a-2)}=\frac{2(16a-15)+13a}{2a(3a-2)}=\frac{15}{2a}\).
8. \(\frac{11}{2x-5}-\frac{9x+5}{x(2x-5)}=\frac{11x-(9x+5)}{x(2x-5)}=\frac1x\).
9. \(\frac{9b-4a}{b(2a-3b)}\).
10. \(\frac{4x^2-25y^2}{xy(5y-2x)}=-\frac{2x+5y}{xy}\).
11. \(\frac{3(a-4c)-6a}{a(a-4c)(a+4c)}=-\frac{3}{a(a-4c)}\).
12. \(\frac{12a-2(3a+4b)}{a(3a-4b)(3a+4b)}=\frac{2}{3a+4b}\).
13. \(\frac{2x+a-x}{2x(a-x)(a+x)}=\frac1{2x(a-x)}\).
14. \(\frac{4p-(c+2p)}{p(c-2p)(c+2p)}=-\frac1{p(c+2p)}\).
15. \(\frac{x-5y+10y}{10y(x-5y)(x+5y)}=\frac1{10y(x-5y)}\).
16. \(\frac{(2c+3a)+4c}{4c(3a-2c)(2c+3a)}=\frac{3(a+2c)}{4c(3a-2c)(2c+3a)}\).

Во всех пунктах предполагается, что исходные знаменатели не равны нулю.