Algebra

Brøker

100

3/5 + 1/4

17/20

200

1/4+2/3*5/2

23/12

300

a/b+(a+b)/a

(a^2+ab+b^2)/(ab)

400

a/(b+2)*(a+2)/(b+1)

(a^2+2a)/(b^2+3b+2)

500

((a+1)/3) / ((2(a+1)/9))

3/2

Potenser

100

3⁴ * 3⁷

3¹¹

200

(2⁵*2^-3)/2

2

300

a^b * (1/a)^b

1

400

(a³)⁶*(ab)^-4

a¹⁴b^-4

500

27^-1/3 * (3a)² * a^-4

3*a^-2

Andengradsligninger

100

x² = 9

x = 3 v x = -3

200

x² - 8x = 0

x = 0 v x = 8

300

x² + 3x + 2 = 0

x = -1 v x = -2

400

4x²  - 16x = 20 

x = 5 v x = -1

500

(x+1)(x+2) = x + 1

x = -1

Kvadratiske lignigssystemer

100

x = y + 2

x + y = 4

(x,y) = (3,1)

200

2x + 3y = 5y + x + 5

2x + 3y = 17

(x,y) = (7,1)

300

3x + 6y = 9x - 12

4y = 4x - 4

(x,y) = Ø

400

3x + y = 5 + x

10 - 4x - 2y = 0 

Sandt for alle (x,y) i de reelle tal, hvor:

y = -2x + 5

500

3x² + 3y = 4

6x² - 2y = -8

(x,y) = Ø

Kvadratsætninger

100

(x+1)²

x² + 1 + 2x

200

(a - 3b)²

a² + 9b² - 6b

300

(x+3)(x-3) - (x-1)²

2x - 10

400

sqrt(x² + 4x + 4)

x+2

500

sqrt(sqrt(x² - 2x + 1) + (x+1)(x-1) + x + 3)

x+1