SOLUTION: When combining terms in a numerator in preparation to divide by a quotient, I'm being told that: {{{ 1-5/x+6/x^2 = (x^2-5x+6)/x^2 = ((x-3)(x-2))/x^2 }}} I'm also being told t

Question 700408: When combining terms in a numerator in preparation to divide by a quotient, I'm being told that:

I'm also being told that:

I understand how you turn step 2 into step 3(factoring), but I have no idea how you turn step 1 into step 2. Help please?
(Eventually the former term is divided by the latter, to get (x-3)/(x-4), but the very first step is where I am stumped.)
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
When you add fractions you must use a common denominator. For example 1/2 + 1/2 = 2/2, but you can't add 1/3 + 1/2 - it's like adding 1 apple to 1 orange.

You must find a common denominator. In 1/2 + 1/3 the common denominator is 6. 6/2=3 so multiply the numerator of 1/2 by 3 (1*3=3) to convert that fraction to 3/6. For 1/3 6/3=2 and 2*1=2 so that converts to 2/6.

Now you can add the fractions 3/6 + 2/6 = 5/6.

The same is true in this problem. is adding/subtracting fractions. You must have a common denominator. In this case the common denominator is .

1 is the same as 1/1. so multiply the numerator by . The converted fraction is .

Convert -5/x ---> and x*-5 is -5x. The converted fraction is .

already has the common denominator so it needs no conversion.

The problem has now become . Since they share the same denominator you can rewrite as the sum/difference of the numerators all over the denominator:

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

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