What sum is equal to 1/x+5 + x^2/x-5

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What sum is equal to 1/x+5 + x^2/x-5

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@Nnesha any ideas?
\[\huge\rm \frac{ 1 }{ x+5 } + \frac{ x^2 }{ x-5 }\] find the common denominator
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 \[\huge\rm \frac{ a } {\color{Red}{ b} }+\frac{ c }{\color{blue}{ d} } =\frac{ a\color{blue}{d}+c\color{Red}{b} }{ bd}\]

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So 1x + 3x/ x+5 x-5
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
make sense ? or do you need an example with numbers ?
yes please. I know this is a simple question but ive been doing algebra since about 8am lol my mind is jumbled
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|
|dw:1444600541383:dw| denominators aren't the same so multiply them
familiar with the foil method ?
Not really
well alright common denominators (x+5)(x-5) |dw:1444600811171:dw| what would you get at the numerator ?
x-5 * 1 and x+5 * x^2
perfect !
\[\huge\rm \frac{ x-5 +x^2 (x+5) }{(x+5)(x-5) }\] (x-5) times 1 = x-5 distribute parentheses x^2 (x+5)
|dw:1444600992770:dw| multiply each term in the parentheses by outside term
|dw:1444611869194:dw|
x^4 ??? x^2 times x^1 =?
x is same as 1x^1 :=)
so it would be x^3 not x^4
yes right
that's it now you can foil (x-5)(x+5) if you want :=)
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
|dw:1444601327889:dw| now multiply by 2nd term
5x and -25
|dw:1444601493094:dw| right now combine like terms 5x -5x cancel
|dw:1444601524920:dw| that would be denomiantor