SOLUTION: simplify y^2-16 / y^2-8y+6

Question 439578: simplify
y^2-16 / y^2-8y+6
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

.......... complete the square

Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics

Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 1:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -8, we know that -8=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .

The highlighted red part must be equal to 6 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (10).

Since the right part 10 is greater than zero, there are two solutions:

, or

Answer: x=7.16227766016838, 0.83772233983162.

use:

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