SOLUTION: i need detailed laymans explanation to simplify rational expression: x2+6x-16 ---------- x2+3x-10

Algebra.Com
Question 227548: i need detailed laymans explanation to simplify rational expression:
x2+6x-16
----------
x2+3x-10

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The simple explanation is that you reduce fractions like:

in exactly the same way you reduce fractions like:

You find common factors, if any, and cancel them.

The difference between the two fractions is that finding the factors of 4 and 8 is a lot easier than finding the factors of and . There are many factoring techniques to learn in order to factor multiple term variable expressions like the ones you have. One of these techniques, called trinomial factoring, happens to work on both the numerator and denominator. Expressions of the form: , like yours, can be factored by answering the question "What are the factors of c (the number at the end) that add up to b (the coefficient in the middle)?"
For the question is "What are the factors of -16 that add up to 6?" After some thought it should be clear that the answer is 8 and -2. So
For the question is "What are the factors of -10 that add up to 3?" The answer: 5 and -2. So

Now our fraction, in factored form, becomes:

We can see now that (x-2) is a factor of both the numerator and denominator. So we can cancel out the common factor:

leaving our reduced fraction:


(NOTE: Don't be tempted to cancel the x's here. They are not factors of the numerator and denominator and only factors may be canceled when reducing fractions!)

RELATED QUESTIONS

Simplify the rational expression: x2 + 3x – 10 _____________ x2 + x – 20 (answered by Nate)
Simplify the rational expression: x2 – 3x – 10/ x2 – x – 20 (answered by BrittanyM)
Simplify the rational expression: x2 + 3x – 10/ x2 + x – 20 (answered by jim_thompson5910)
simplify the rational expression x2 – 6x + 8 ------------- x2 – 4 please help (answered by checkley75)
Simplify the rational expression. -6x x-x2 (answered by rapaljer)
Simplify the rational expression: x2 – 6x + 8 ----------- x2 –... (answered by Earlsdon)
Simplify the rational expression: x2 – 6x – 7 ---------------- x2 – 1 (answered by jojo14344)
please show me how to do this. Simplify the rational expression: x2 – 3x – 10 x2 – x (answered by jim_thompson5910)
Rational and Radical Expressions 1. Simplify the rational expression: x2 – 6x – 7 (answered by gladley)