SOLUTION: When multipling the numerator and denominator by a factor of 1, does the fraction change in value in the following expression? What is the first step for this problem? This is a co

Question 553449: When multipling the numerator and denominator by a factor of 1, does the fraction change in value in the following expression? What is the first step for this problem? This is a confusing expression.Explain each step.
3/(x-4)+8/(x-4)^2
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
apparently they want you to simplify this expression.
the expression is:
3/(x-4) + 8/(x-4)^2
to simplify this expression, you need to be able to combine the terms using a common denominator.
the common denominator will be (x-4)^2.
to get the left term with a denominator of (x-4)^2, you need to multiply the numerator and denominator by (x-4)/(x-4).
note that (x-4)/(x-4) is equal to 1.
if you multiply anything by 1, the expression remains the same, i.e. is unchanged.
this makes 3/(x-4) have exactly the same value as 3*(x-4)/(x-4)^2 because if you cancel out the common (x-4) in the numerator and the denominator you are left with 3/(x-4) which was the original term.
so you multiply 3/(x-4) by (x-4)/(x-4) to get 3(x-4)/(x-4)^2
you now have a common denominator of (x-4)^2 which allows you to combine the fractions together to get:
(3(x-4) + 8)/(x-4)^2 which you can then simplify to:
(3x-12+8)/(x-4)^2 which simplifies further to:
(3x-4)/(x-4)^2
i believe that's as far as you can go with this, i.e. it does not simplify any further.

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