SOLUTION: Please help me begin to solve: 1-2/x-8/x^2=0

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Question 77539: Please help me begin to solve:
1-2/x-8/x^2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1-2%2Fx-8%2Fx%5E2=0

x%5E2%281-2%2Fx-8%2Fx%5E2%29=x%5E2%280%29 Multiply both sides by x%5E2, this eliminates the denominator

x%5E2-2x-8=0 Distribute x%5E2 on both sides

Now factor the quadratic:
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B-2%2Ax%2B-8, first we need to ask ourselves: What two numbers multiply to -8 and add to -2? Lets find out by listing all of the possible factors of -8


Factors:

1,2,4,8,

-1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -8.

(-1)*(8)=-8

(-2)*(4)=-8

Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

||||
First Number|Second Number|Sum
1|-8|1+(-8)=-7
2|-4|2+(-4)=-2
-1|8|(-1)+8=7
-2|4|(-2)+4=2
We can see from the table that 2 and -4 add to -2.So the two numbers that multiply to -8 and add to -2 are: 2 and -4 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=2 and b=-4 So the equation becomes: (x+2)(x-4) Notice that if we foil (x+2)(x-4) we get the quadratic 1%2Ax%5E2%2B-2%2Ax%2B-8 again


Now set each factor equal to zero

x%2B2=0
x=-2
x-4=0
x=4
So our solution is:
x=-2 or x=4