A1.
(x²+3x)/2+(x-3x²)/8=2x
x²/8+13x/8=2x
x²/8-3x/8=0
(x(x-3))/8=0
x(x-3)=0
x-3=0 or x=0
x=3 x=0
2.
A2.
x²/(3-x)=2x/(x-3)
x²=2x
x(x-2)=0
x-2=0 or x=0
x=2 or x=0
2+0=2
2.
A3.
(x²+3x)/(x-4)=(x²-x)/(4-x)
x≠4
(4-x)(x²+3x)=(x-4)(x²-x)
-x³+x²+12x=x³-5x²+4x
-2x³+6x²+8x=0
-2x(x-4)(x+1)=0
x(x-4)(x+1)=0
x=0 or x-4=0 or x+1=0
x=0 or x=4 not or x=-1
x=0 or x=-1
3.
A4.
(5y-2)/(2y+1)=(3y+2)/(y+3)
(y+3)(5y-2)=(2y+1)(3y+2)
5y²+13y-6=6y²+7y+2
-y²+6y-8=0
-(y-4)(y-2)=0
(y-4)(y-2)=0
y-4=0 or y-2=0
y=4 or y=2
(4+2)/2=3
3.
A5.
(4x²-11x-3)/(3-x)=0
x≠3
4x²-11x-3=0
(x-3)(4x+1)=0
x-3=0 or 4x+1=0
x=3 not or x=-1/4
x=-1/4
4.
B1.
(7a-6)/(a³+27)=1/(a²-3a+9)-1/(a+3)
a≠-3
7a-6=-a²+4a-6
a²+3a=0
a(a+3)=0
a=0 or a+3=0
a=0 or a=-3 not
a=0
B2.
y=4x and y=7/(x+1)-1
4x=7/(x+1)-1
x≠-1
4x=(6-x)/(x+1)
4x(x+1)=6-x
4x²+4x=6-x
4x²+5x-6=0
(x+2)(4x-3)=0
x+2=0 or 4x-3=0
x=-2 or x=3/4
y=(-2)*4=-8
y=(3/4)*4=3
A(-2;-8)
B(3/4;3)
C1.
x²+3x=8/(x²+3x-2)
(x²+3x)(x²+3x-2)=8
x⁴+6x³+7x²-6x-8=0
(x-1)(x+1)(x+2)(x+4)=0
x-1= or x+1=0 or x+2=0 or x+4=0
x=1 or x=-1 or x=-2 or x=-4