2,

a,

`x/2+x/9=44`

`(9x+2x)/18=44`

`(11x)/18=44`

`x/18=4`

x = 72

b,

`(x+1)/6-(x-1)/4=0`

`(2(x+1)-3(x-1))/12=0`

2x+2-3x+3=0

-x+5=0

x = 5

c,

`2x-(5/7*x-3/4*x)=57`

`2x-((20-21)x)/28`=57

`(57x)/28=57`

x = 28

d,

`6-(6x-4)/5=2x+(2-5x)/3`

`(90-(18x-12))/30=(30x+(10-25x))/30`

102-18x = 10+5x

23x = 92

x = 4

e,

`3x-(x+2)/4-(3x-2)/2=1-(x-1)/3`

`(36x-3x-6-18x+12)/12=(12-4x+4)/12`

15x+6 = 16-4x

19x = 10

x = `10/19`

f,

`x-(6-2x)/3=2x-4-(x+3)/2`

`(6x-12+4x)/6=(12x-24-3x-9)/6`

10x-12 = 9x-33

x = -21

g,

`x+(x+1)/4=2x+(5-3x)/2-(x-3)/8`

`(8x+2x+2)/8=(16x+20-12x-2x+6)/8`

10x+2 = 2x+26

8x = 24

x = 3

h,

`1-(6-2x)/3=x-(x+3)/2`

`(6-12+4x)/6=(6x-3x-9)/6`

4x-6 = 3x-9

x = -3

3,

a,

`x/(x-5)=5/(x-5)`

Felt: `x ne 5`

szorzunk a nevezővel.

x = 5

Mivel kizártuk, ezért nincs megoldás.

b,

`2/x+5/x=1`

Felt: `x ne 0`

`(2+5)/x` = 1

`7/x=1` /*x

x = 7

c,

`(x+3)/(4x)-1/2=(x-1)/(12x)+1/12`

Felt: `x ne 0`

`(3(x+3)-6x)/(12x)=((x-1)+x)/(12x)` (*12x)

3x+9-6x = 2x-1

-3x+9 = 2x-1

5x = 10

x = 2

d,

`(12x-9)/(3x-2)-(4x-5)/(2x-3)=2`

Felt: `x ne 2/3`, `x ne 3/2`

`(12x-9)*(2x-3)-(3x-2)*(4x-5)=2*(3x-2)*(2x-3)`

`24x^2-18x-36x+27-12x^2+8x+15x-10=2*(6x^2-4x-9x+6)`

`cancel(12x^2)-31x+17=cancel(12x^2)-26x+12`

5x = 5

x = 1

e,

`2x+(x^2-4)/(x+2)=1`

Felt: `x ne -2`

`2x+((x-2)*cancel(x+2))/(cancel(x+2))=1`

2x+x-2 = 1

3x = 3

x = 1

f,

`(9-x)/(x-4)=5/(x-4)+3`

Felt: `x ne 4`

`(9-x)/(x-4)=5/(x-4)+3*(x-4)`

9-x = 5+3x-12

4x = 16

x = 4; de a kezdeti feltétel miatt ez nem megoldás.