The sum of two numbers is 70 and their difference is 30. Find the two numbers
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Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form 
. To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
In the denominator we have a difference of squares:
Now we can rewrite our function:
From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at
and 
We can conclude that the graphic of our rational function is:
In the denominator we have a difference of squares:
Now we can rewrite our function:
From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at
We can conclude that the graphic of our rational function is:
