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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

Question 700408: When combining terms in a numerator in preparation to divide by a quotient, I'm being told that:
+1-5%2Fx%2B6%2Fx%5E2+=+%28x%5E2-5x%2B6%29%2Fx%5E2+=+%28%28x-3%29%28x-2%29%29%2Fx%5E2+
I'm also being told that:
+1-6%2Fx%2B8%2Fx%5E2+=+%28x%5E2-6X%2B8%29%2Fx%5E2+=+%28%28x-4%29%28x-2%29%29%2Fx%5E2+
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) About Me  (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. 1-+5%2Fx+-6%2Fx%5E2 is adding/subtracting fractions. You must have a common denominator. In this case the common denominator is x%5E2.


1 is the same as 1/1. x%5E2+%2F+1+=+x%5E2 so multiply the numerator by x%5E2. The converted fraction is x%5E2+%2F+x%5E2.


Convert -5/x --->x%5E2+%2F+x+=+x and x*-5 is -5x. The converted fraction is -5x%2Fx%5E2.


6%2Fx%5E2 already has the common denominator so it needs no conversion.


The problem has now become x%5E2+%2F+x%5E2+-+5x%2Fx%5E2+%2B+6%2Fx%5E2. Since they share the same denominator you can rewrite as the sum/difference of the numerators all over the denominator:


%28x%5E2-5x%2B6%29%2Fx%5E2

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.)