SOLUTION: (x-6x+9)/(x-3)

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Question 216079: (x-6x+9)/(x-3)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-6x%2B9%29%2F%28x-3%29

Step 1. Look at the numerator x%5E2-6x%2B9.

Step 2. Need to integers m and n whose sum is -6 and product is 9.

Step 3. The two integers are -3 and -3. We can factor through grouping where -6x=-3x-3x. We can also recognize that the trinomial is a perfect square, that is x%5E2-6x%2B9=%28x-3%29%5E2. Nevertheless the following steps, will show the technique of grouping.

x%5E2-6x%2B9=%28x%5E2-3x%29%2B%28-3x%2B9%29=x%28x-3%29-3%28x-3%29

Factor (x-3) from both groups

x%5E2-6x%2B9=%28x-3%29%5E2

Step 4. Now substitute the expression in Step 3 with %28x-3%29%5E2

%28x%5E2-6x%2B9%29%2F%28x-3%29=%28x-3%29%5E2%2F%28x-3%29

Note we can cancel the factor (x-3) in the numerator and denominator.

%28x%5E2-6x%2B9%29%2F%28x-3%29=x-3

Step 4. ANSWER: %28x%5E2-6x%2B9%29%2F%28x-3%29=x-3

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J