SOLUTION: The perimeter of a triangle is 2x + 5. Find the 3rd side if the other two sides are X^2-6 over x-6 and x^2 - 5x - 9 over x-6. pleasee help me? :)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The perimeter of a triangle is 2x + 5. Find the 3rd side if the other two sides are X^2-6 over x-6 and x^2 - 5x - 9 over x-6. pleasee help me? :)      Log On


   

Question 199269: The perimeter of a triangle is 2x + 5. Find the 3rd side if the other two sides are X^2-6 over x-6 and
x^2 - 5x - 9 over x-6.
pleasee help me? :)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, here's the strategy!
Add together the two given sides and subtract this sum from the given perimeter to get the third side.
Here's the action!
Add the two given sides:
%28%28x%5E2-6%29%2F%28x-6%29%29%2B%28%28x%5E2-5x-9%29%2F%28x-6%29%29 Since we have a common denominator (x-6), we can add the two fractions.
%28%28x%5E2-6%29%2B%28x%5E2-5x-9%29%29%2F%28x-6%29 Simplify the numerator.
%282x%5E2-5x-15%29%2F%28x-6%29 Now we subtract this from the given perimeter of %282x%2B5%29.
%282x%2B5%29-%28%282x%5E2-5x-15%29%2F%28x-6%29%29 We need to get the first term over a common denominator of %28x-6%29 so we'll multiply the numerator and the denominator by %28x-6%29
%28%282x%2B5%29%28x-6%29%2F%28x-6%29%29-%28%282x%5E2-5x-15%29%2F%28x-6%29%29 Now simplify the numerator of the first fraction by performing the indicated multiplication using the FOIL method.
%28%282x%5E2-7x-30%29%2F%28x-6%29%29-%28%282x%5E2-5x-15%29%2F%28x-6%29%29 Now we can do the subtraction since we have both fractions over a common denominator.
%282x%5E2-7x-30-2x%5E2%2B5x%2B15%29%2F%28x-6%29 Simplify the numerator.
%28-2x-15%29%2F%28x-6%29 or highlight%28-%28%282x%2B15%29%2F%28x-6%29%29%29...this is the length of the third side of the triangle.
We can check this solution by adding the three sides to see if we get the given perimeter of 2x%2B5:
%28x%5E2-6%29%2F%28x-6%29%2B%28x%5E2-5x-9%29%2F%28x-6%29%2B%28-%282x%2B15%29%2F%28x-6%29%29
%28x%5E2-6%2Bx%5E2-5x-9-2x-15%29%2F%28x-6%29 Simplify the numerator.
%282x%5E2-7x-30%29%2F%28x-6%29 Factor the numerator.
%282x%2B5%29cross%28%28x-6%29%29%2F%28cross%28%28x-6%29%29%29 Cancel the indicated factors to leave you with:
2x%2B5...and this is the given perimeter.