Question

Va rog la exercitiul 12 numai b si d,la exercitiul 13 numai b,c si de

Answer 1

12b
(x²+2x+2y²-y⁴)/(x²-xy²+2y²-4)=
=(x²-y⁴+2x+2y²)/(x²-4-xy²+2y²)=
=[(x-y²)(x+y²)+2(x+y²)]/[(x-2)(x+2)-y²(x-2)]=
=(x+y²)(x-y²+2)/(x-2)(x+2-y²)=
=(x+y²)/(x-2)

12d
[a/(a-b)-ab/(a²-b²)] : 4a²/(a²-2ab+b²)=
=[a/(a-b)-ab/(a-b)(a+b)] : 4a²/(a-b)²=
=[a(a+b)-ab]/(a-b)(a+b) × (a-b)²/4a²=
=(a²+ab-ab)/(a+b) × (a-b)/4a²=
=a²/(a+b) × (a-b)/4a²=
=1/(a+b) × (a-b)/4=
=(a-b)/4(a+b)


13b
(x+y)/(x+2y) :[x/(x-2y) + y²/(x²-4y²) =
=(x+y)/(x+2y) :[x/(x-2y) + y²/(x-2y)(x+2y) =
=(x+y)/(x+2y) :(x²+2xy+y²)/(x-2y)(x+2y) =
=(x+y)/(x+2y) :(x+y)²/(x-2y)(x+2y) =
=(x+y)/(x+2y) :(x+y)/(x-2y) =
=(x+y)/(x+2y) × (x-2y)/(x+y) =
=(x-2y)/(x+2y)
x=-1,8    y=0,6
(-1,8-2×0,6)/(-1,8+2×0,6)=(-3)/(-0,6)=5


13c
x²/(x²-2y) : [2xy/(x²-4y²) - y/(x+2y)]=
=x²/x(x-2y) : [2xy/(x-2y)(x+2y) - y/(x+2y)]=
=x/(x-2y) : (2xy-xy+2y²)/(x-2y)(x+2y)=
=x/(x-2y) : (xy+2y²)/(x-2y)(x+2y)=
=x/(x-2y) : y(x+2y)/(x-2y)(x+2y)=
=x/(x-2y) : y/(x-2y)=
=x/(x-2y) × (x-2y) /y=
=x/y
x=-1,8    y=0,6
(-1,8)/0,6)=-3

13d
[2xy/(x²-9y²)-y/(x-3y)] :y²/(x²+3xy)=
=[2xy/(x-3y)(x+3y)-y/(x-3y)] :y²/x(x+3y)=
=(2xy-xy-3y²)/(x-3y)(x+3y) × x(x+3y)/y²=
=(xy-3y²)/(x-3y) × x/y²=
=y(x-3y)/(x-3y) × x/y²=
=y/1 × x/y²=
=x/y
x=-1,8    y=0,6
(-1,8)/0,6)=-3