SOLUTION: can you help me express in simplest form x^2/ over x+10 plus 9x-10 over x+10

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Question 77366: can you help me express in simplest form
x^2/
over
x+10
plus
9x-10
over
x+10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2F%28x%2B10%29%2B%289x-10%29%2F%28x%2B10%29 Since we have a common denominator, we can add the fractions

%28x%5E2%2B9x-10%29%2F%28x%2B10%29

Now factor the numerator:

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B9%2Ax%2B-10, first we need to ask ourselves: What two numbers multiply to -10 and add to 9? Lets find out by listing all of the possible factors of -10


Factors:

1,2,5,10,

-1,-2,-5,-10,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -10.

(-1)*(10)=-10

(-2)*(5)=-10

Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9

||||
First Number|Second Number|Sum
1|-10|1+(-10)=-9
2|-5|2+(-5)=-3
-1|10|(-1)+10=9
-2|5|(-2)+5=3
We can see from the table that -1 and 10 add to 9.So the two numbers that multiply to -10 and add to 9 are: -1 and 10 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: %28x%2Ba%29%28x%2Bb%29substitute a=-1 and b=10 So the equation becomes: (x-1)(x+10) Notice that if we foil (x-1)(x+10) we get the quadratic 1%2Ax%5E2%2B9%2Ax%2B-10 again


So the equation becomes

%28%28x-1%29%28x%2B10%29%29%2F%28x%2B10%29

%28%28x-1%29cross%28x%2B10%29%29%2Fcross%28x%2B10%29 Cancel like terms

x-1
So the whole thing reduces to x-1 in other words:
x%5E2%2F%28x%2B10%29%2B%289x-10%29%2F%28x%2B10%29=x-1