50. Распрости ихтигеор кучен. а) 0,4x²t²z/(0,2xy³z²); б) 0,8a⁷c³/(0,4a⁶c⁴); в) 3ad(x+y)²/(9a²(x+y)); г) 0,1x³y⁵(a+b)/(3x²y³(a+b)³); д) (x²−2xy)/(xy−2y²); е) (1−x²)/(x²−x); ж) (x⁶−y⁶)/(x³−y³); з) (3a−6b+9c)/(5a−10b+15c); и) xy/(x²y−y²x); к) (4k²−p²)/(p−2k)²; л) (4+2a+a²)/(a³−8); м) (4a³−25a²)/(2a²−5ab).

Разложим числители и знаменатели на множители и сократим общие множители.

1. а) \(\dfrac{0.4x^2t^2z}{0.2xy^3z^2}=\dfrac{2xt^2}{y^3z}\).
2. б) \(\dfrac{0.8a^7c^3}{0.4a^6c^4}=\dfrac{2a}{c}\).
3. в) \(\dfrac{3ad(x+y)^2}{9a^2(x+y)}=\dfrac{d(x+y)}{3a}\).
4. г) \(\dfrac{0.1x^3y^5(a+b)}{3x^2y^3(a+b)^3}=\dfrac{xy^2}{30(a+b)^2}\).
5. д) \(\dfrac{x^2-2xy}{xy-2y^2}=\dfrac{x(x-2y)}{y(x-2y)}=\dfrac{x}{y}\).
6. е) \(\dfrac{1-x^2}{x^2-x}=\dfrac{(1-x)(1+x)}{x(x-1)}=-\dfrac{x+1}{x}\).
7. ж) \(\dfrac{x^6-y^6}{x^3-y^3}=\dfrac{(x^3-y^3)(x^3+y^3)}{x^3-y^3}=x^3+y^3\).
8. з) \(\dfrac{3a-6b+9c}{5a-10b+15c}=\dfrac{3(a-2b+3c)}{5(a-2b+3c)}=\dfrac35\).
9. и) \(\dfrac{xy}{x^2y-y^2x}=\dfrac{xy}{xy(x-y)}=\dfrac1{x-y}\).
10. к) \(\dfrac{4k^2-p^2}{(p-2k)^2}=\dfrac{(2k-p)(2k+p)}{(p-2k)^2}=-\dfrac{2k+p}{p-2k}\).
11. л) \(\dfrac{4+2a+a^2}{a^3-8}=\dfrac{a^2+2a+4}{(a-2)(a^2+2a+4)}=\dfrac1{a-2}\).
12. м) \(\dfrac{4a^3-25a^2}{2a^2-5ab}=\dfrac{a^2(4a-25)}{a(2a-5b)}=\dfrac{a(4a-25)}{2a-5b}\).

Ответ: а) \(\dfrac{2xt^2}{y^3z}\); б) \(\dfrac{2a}{c}\); в) \(\dfrac{d(x+y)}{3a}\); г) \(\dfrac{xy^2}{30(a+b)^2}\); д) \(\dfrac{x}{y}\); е) \(-\dfrac{x+1}{x}\); ж) \(x^3+y^3\); з) \(\dfrac35\); и) \(\dfrac1{x-y}\); к) \(-\dfrac{2k+p}{p-2k}\); л) \(\dfrac1{a-2}\); м) \(\dfrac{a(4a-25)}{2a-5b}\).