## anonymous one year ago What sum is equal to 1/x+5 + x^2/x-5

1. anonymous

@Nnesha any ideas?

2. Nnesha

$\huge\rm \frac{ 1 }{ x+5 } + \frac{ x^2 }{ x-5 }$ find the common denominator

3. Nnesha

find common denominator multiply the numerator of first fraction by the denominator of 2nd fraction multiply the numerator of 2nd fraction by the denominator of first fraction here is an example $\huge\rm \frac{ a } {\color{Red}{ b} }+\frac{ c }{\color{blue}{ d} } =\frac{ a\color{blue}{d}+c\color{Red}{b} }{ bd}$

4. anonymous

So 1x + 3x/ x+5 x-5

5. Nnesha

hmm that looks wrong when the denominators are not the same to get the common denominator multiply denominators of both fractions just like in the example i gave you

6. Nnesha

make sense ? or do you need an example with numbers ?

7. anonymous

yes please. I know this is a simple question but ive been doing algebra since about 8am lol my mind is jumbled

8. Nnesha

alright i'll give you an example $\huge\rm \frac{ 2 }{ 3 } +\frac{ 4 }{ 5 }$ denominators aren't the same so i should multiply them 3 times 5 = 15 so 15 is my common denominator $\frac{ ??? + ?? }{ 15 }$ when we convert two fractions to one we should multiply the numerator of 1st fraction with the denominator of 2nd fraction and multiply the numerator of 2nd fraction with the denominator of first fracton just like cross multiplication but we should keep the positive sign |dw:1444600450247:dw|

9. Nnesha

|dw:1444600541383:dw| denominators aren't the same so multiply them

10. Nnesha

familiar with the foil method ?

11. anonymous

Not really

12. Nnesha

well alright common denominators (x+5)(x-5) |dw:1444600811171:dw| what would you get at the numerator ?

13. anonymous

x-5 * 1 and x+5 * x^2

14. Nnesha

perfect !

15. Nnesha

$\huge\rm \frac{ x-5 +x^2 (x+5) }{(x+5)(x-5) }$ (x-5) times 1 = x-5 distribute parentheses x^2 (x+5)

16. Nnesha

|dw:1444600992770:dw| multiply each term in the parentheses by outside term

17. anonymous

|dw:1444611869194:dw|

18. Nnesha

x^4 ??? x^2 times x^1 =?

19. Nnesha

x is same as 1x^1 :=)

20. anonymous

so it would be x^3 not x^4

21. Nnesha

yes right

22. Nnesha

that's it now you can foil (x-5)(x+5) if you want :=)

23. Nnesha

but anywyas let's learn how to foil |dw:1444601278891:dw| write one parentheses at the top of the box and one at left side multiply each left term by the top one

24. Nnesha

|dw:1444601327889:dw| now multiply by 2nd term

25. anonymous

5x and -25

26. Nnesha

|dw:1444601493094:dw| right now combine like terms 5x -5x cancel

27. Nnesha

|dw:1444601524920:dw| that would be denomiantor