a) Dziedzina: x≠0
4x + 5 / 2x = 4 /*2x
4x+5= 8x
4x-8x= -5
-4x= -5 /:(-4)
x= 5/4
b) x≠0
15/x = x-2 /*x
15= (x-2)x
15- (x-2)x= 0
15- x² + 2x = 0
-x² + 2x + 15 = 0
∆= 2²- 4 * (-1) * 15 = 64
√∆ = 8
x1 = -2-8/ 2* (-1) = 5
x2 = -2+8/ 2* (-1) = -3
c) dziedzina: x≠1
x= 7x -4 / 2x-2 /* (2x-2)
(2x-2)x= 7x-4
(2x-2)x -7x +4 =0
2x²-9x +4=0
∆= (-9)² -4* 2* 4=49
√∆ = 7
x1= 9-7/ 2*2 = ½
x2= 9+7/ 2*2= 4
d) dziedzina: x≠0
x+2= 2-2x/x /*x
(x+2)x= 2-2x
(x+2)x-2+2x=0
x²+2x-2+2x=0
x²+4x-2=0
∆=4²-4* 1 *(-2)=24
√∆= 2√6
x1= -4-2✓6/2*1 = -2√6
x2= -4+2√6/2*1= -2+√6
e) dziedzina: x≠-1
2x+7/ x+1 = x+1 /*(x+1)
2x+7=(x-1)(x+1)
2x+7-(x-1)(x+1)=0
2x+7-(x²-1)=0
2x+7-x²+1=0
-x²+2x+8=0
∆=2²-4* (-1) *8 = 36
√∆= 6
x1= -2-6/ 2*(-1) = 4
x2= -2+6/2*(-1)= -2
f) dziedzina: x≠ -⅓
6x+2/ -1-3x = -2x -2
-2(-3x-1)/ -1-3x= -2x -2 (skracamy)
-2= -2x-2
-2x=0 /:(-2)
x=0
