Question

срочно, только четные ​

Answer 1

$170.1)\ \ \dfrac{x-\sqrt{xy}+y}{\sqrt{x}-\sqrt{y}}=\dfrac{(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}=\dfrac{(\sqrt{x})^3+(\sqrt{y})^3}{(\sqrt{x})^2-(\sqrt{y})^2}=\dfrac{\sqrt{x^3}+\sqrt{y^3}}{x-y}\\\\\\2)\ \ \dfrac{9+3\sqrt{a}+a}{3+\sqrt{a}}=\dfrac{(9+3\sqrt{a}+a)(3-\sqrt{a})}{(3+\sqrt{a})(3-\sqrt{a})}=\dfrac{3^3-\sqrt{a^3}}{9-a}=\dfrac{27-\sqrt{a^3}}{9-a}$

$4.\ \ \dfrac{a^2b+2a\sqrt{b}+4}{a\sqrt{b}+2}=\dfrac{(a^2b+2a\sqrt{b}+4)(a\sqrt{b}-2)}{(a\sqrt{b}+2)(a\sqrt{b}-2)}=\dfrac{(a\sqrt{b})^3-2^3}{(a\sqrt{b})^2-2^2}=\dfrac{a^3\sqrt{b^3}-8}{a^2b-4}$

$6.\ \ \dfrac{a+\sqrt{b}}{a\sqrt{b}}=\dfrac{(a+\sqrt{b})\cdot \sqrt{b}}{a\sqrt{b}\cdot \sqrt{b}}=\dfrac{(a+\sqrt{b})\cdot \sqrt{b}}{ab}=\dfrac{a\sqrt{b}+b}{ab}\\\\\\8.\ \ \dfrac{\sqrt{m\, n}+1}{mn+\sqrt{mn}+1}=\dfrac{(\sqrt{mn}+1)(\sqrt{mn}-1)}{(mn+\sqrt{mn}+1)(\sqrt{mn}-1)}=\dfrac{mn-1}{\sqrt{m^3n^3}-1}=\\\\\\=\dfrac{(mn-1)(\sqrt{m^3n^3}+1)}{(\sqrt{m^3n^3}-1)(\sqrt{m^3n^3}+1)}=\dfrac{(mn-1)(\sqrt{m^3n^3}+1)}{m^3n^3-1}$

$10.\ \ \dfrac{1}{\sqrt2+\sqrt3+1}=\dfrac{(\sqrt2+\sqrt3)-1}{((\sqrt2+\sqrt3)+1)((\sqrt2+\sqrt3)-1)}=\dfrac{\sqrt2+\sqrt3-1}{(\sqrt2+\sqrt3)^2-1}=$

$=\dfrac{\sqrt2+\sqrt3-1}{(5+2\sqrt6)-1}=\dfrac{\sqrt2+\sqrt3-1}{2\, (2+\sqrt6)}=\dfrac{(\sqrt2+\sqrt3-1)(2-\sqrt6)}{2\, (2+\sqrt6)(2-\sqrt6)}=\\\\\\=\dfrac{(\sqrt2+\sqrt3-1)(2-\sqrt6)}{2\, (4-6)}=\dfrac{(\sqrt2+\sqrt3-1)(2-\sqrt6)}{-4}=\\\\\\=-0,25\cdot (\sqrt2+\sqrt3-1)(2-\sqrt6)$

$12.\ \ \dfrac{x-2\sqrt{3x}+3}{\sqrt{x}+\sqrt3}= \dfrac{(\sqrt{x}-\sqrt3)^2(\sqrt{x}-\sqrt3)}{(\sqrt{x}+\sqrt3)(\sqrt{x}-\sqrt3)}=\dfrac{(\sqrt{x}-\sqrt{3})^3}{x-3}$    

Answer 2

2) (3²+3√а+а)/(3+√а)=(3²+3√а+а)(3-√а)/(3+√а)(3-√а)=(27-√а³)/(3-а)

4)(а²b+2a√b+4)/(a√b+2)=(а²b+2a√b+4)(a√b-2)/(a√b+2)*(a√b-2)=

(a³b√b-8)/(a²b-4)

6)(a+√b)/(a√b)=(a+√b)√b/(ab)=(b+a√b)/(ab)

8) (√mn+1)/(mn+√mn+1)= (√mn-1)(√mn+1)/(mn+√mn+1)(√mn-1)=

(mn-1)/(√m³n³-1)=(√m³n³+1)(mn-1)/(m³n³-1)

10) 1/(√2+√3+1)=(-√2+√3+1)/((√2+√3+1)*(-√2+√3+1))=

(-√2+√3+1)/(-2+2√3+4)=(-√2+√3+1)/(2+2√3)=(-√2+√3+1)*(2-2√3)/(4-4*3)=

(-√2+√3+1)*(-1+√3)/4

12) (x-2√(3x)+3)/(√x+√3))=((√x-√3))²/(√x+√3)=(√x-√3)((√x-√3))²/(x-3)=(√x-√3)³/(x-3)