document.write( "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
\n" ); document.write( "x^2 - 5x - 9 over x-6.\r
\n" ); document.write( "\n" ); document.write( "pleasee help me? :)
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Algebra.Com's Answer #149726 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Ok, here's the strategy!
\n" ); document.write( "Add together the two given sides and subtract this sum from the given perimeter to get the third side.
\n" ); document.write( "Here's the action!
\n" ); document.write( "Add the two given sides:
\n" ); document.write( "\"%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.
\n" ); document.write( "\"%28%28x%5E2-6%29%2B%28x%5E2-5x-9%29%29%2F%28x-6%29\" Simplify the numerator.
\n" ); document.write( "\"%282x%5E2-5x-15%29%2F%28x-6%29\" Now we subtract this from the given perimeter of \"%282x%2B5%29\".
\n" ); document.write( "\"%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\"
\n" ); document.write( "\"%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.
\n" ); document.write( "\"%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.
\n" ); document.write( "\"%282x%5E2-7x-30-2x%5E2%2B5x%2B15%29%2F%28x-6%29\" Simplify the numerator.
\n" ); document.write( "\"%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.
\n" ); document.write( "We can check this solution by adding the three sides to see if we get the given perimeter of \"2x%2B5\":
\n" ); document.write( "\"%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\"
\n" ); document.write( "\"%28x%5E2-6%2Bx%5E2-5x-9-2x-15%29%2F%28x-6%29\" Simplify the numerator.
\n" ); document.write( "\"%282x%5E2-7x-30%29%2F%28x-6%29\" Factor the numerator.
\n" ); document.write( "\"%282x%2B5%29cross%28%28x-6%29%29%2F%28cross%28%28x-6%29%29%29\" Cancel the indicated factors to leave you with:
\n" ); document.write( "\"2x%2B5\"...and this is the given perimeter.
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