2. 04 is zero, but 40 is undefined

3. The reciprocal of a number or expression is its multiplicative inverse.

4. The reciprocal of 43 is 34

5. The reciprocal of 6 is 16

6. The reciprocal of x+1 is 1x+1

7. Multiply fractions

8. 23 x 52=106 = 53

9. Dividing fractions

10. 23 ÷ 52

11. =23 x 25=415

12. Adding fractions

13. 23+ 53=2 + 53=73

14. 25+ 58=16 + 2540=4140

16. Subtracting fractions

17. Subtracting fractions works like adding fractions except that instead of adding you subtract.

18. Substitution

19. An algebraic expression or just expression is something like xyz or a3p2q-6, basically without equal sign (if it has an equal sign, it is an equation).

20. If we substitute x = (a + b) to x2yz we will have (a+b)2yz

21. Canceling fractions

22. x5y2x3yz=x2yz

23. You can cancel fractions only when it has unbroken chain or multiplication through the entire numerator and the entire denominator.

24. a2b2xy-pq4(c+d)ab4z(xy-pq)3=axy-pq(c+d)b2z

25. Absolute Value

26. Absolute value just turns the negative number into a positive number and does nothing to a positive number or zero.

27. |-6| = 6

29. 3x2=x23

31. Factoring

32. Difference of two squares: a2-b2=a+b(a-b)

33. Sum of two cubes: a3+b3=a+b(a2-ab+b2)

34. Difference of two cubes: a3-b3=a-b(a2+ab+b2)

36. x-x3-x2+9(2x2-7x-8)

37. 1x-y+3x+yx2-y2

38. 4x-7-3x+7

40. 3x2-5x-2(x2-4x+3)

41. 4x-7+2x49-x2

42. 6x4-x-24+x

43. x-1 - 2x+2 x + 2 - 2x-1Reference: Calculus for Dummies by Mark Ryan © Wiley Pub., 2003<br />