Question

Doprowadź do najprostszej postaci:
(a²+2ab+b²)/a²-b²=
(a²-5)/(a+√5)=
(x²+√y*x)/(x³-xy)=

Answer 1

[a²+2ab+b²]/[a²-b²]=

[a+b]²/[a+b][a-b]=

[a+b][a+b]/[a+b][a-b]=

[a+b]/[a-b]

 

[a²-5]/[a+√5]=

[a+√5][a-√5]/[a+√5]=

a-√5

 

[x²+√y ×x]/[x³-xy]=

[x(x+√y)]/[x(x²-y)]=[x(x+√y)]/[x(x+√y)(x-√y)]=

1/[x-√y]

tu by można jeszcze usunąc niewymiernośc

Answer 2

(a²+2ab+b²)/a²-b²=(a+b)^2/(a-b)(a+b)=(a+b)/(a-b)
(a²-5)/(a+√5)=(a-√5)(a+√5)/(a+√5)=a-√5
(x²+√y*x)/(x³-xy)=x(x+√y)/x(x^2-y)=(x+√y)/(x^2-y)