SOLUTION: find all the values of x satisfying the given conditions 1 2 -4 y1= --- , ----, ---------, and y1+y2=y3 x+7 x+3 x^2+10+21

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Question 107637: find all the values of x satisfying the given conditions
1 2 -4
y1= --- , ----, ---------, and y1+y2=y3
x+7 x+3 x^2+10+21

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your problem as written doesn't make sense, but I'm going to make an assumption that does and go with that. What I think you meant was:

y1=1%2F%28x%2B7%29, y2=2%2F%28x%2B3%29, y3=%28-4%29%2F%28x%5E2%2B10x%2B21%29, and y1%2By2=y3

That means we can say:

%281%2F%28x%2B7%29%29%2B%282%2F%28x%2B3%29%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29

To add the two terms on the left side, we need a Lowest Common Denominator, given by:

%28x%2B7%29%28x%2B3%29=x%5E2%2B10x%2B21

Now we have:



Simplify:

%283x%2B17%29%2F%28x%5E2%2B10x%2B21%29=%28-4%29%2F%28x%5E2%2B10x%2B21%29

Since the denominators are equal on both sides, the numerators must be equal as well for the statement to be true, therefore:

3x%2B17=-4
3x=-21
x=-21%2F3=-7

But that causes a problem because -7 is not in the domain of either the y1 or y3 functions. x=-7 leads to a zero denominator in each case. Therefore, there are no values of x that satisfy the given conditions. Presuming my assumptions about the construct of the original problem were correct, that is.