algebra boubt

Question

please read my doubt carefully

 

 

(2*m^2-5*m-12)/(m^2+m-20)            first example

 

(21*x^3*y-6*x^2*y^4+3*x*y)/(3*x*y)         second example

 

in second ex first term we can cancel 21x^3y     then ans is "7x^2"

                                                        3xy                 

but first ex first term  2m^2    then why we shouldt cross out m numeratior and m denominator. in my book reason state

                                     m 

that because term are added but second ex we have also add and subtraction sign then also we cross out

 

i want the rule when we should cancel terms and when dont please explain me

                                

Answer 1

Amey, let's break it down.

 

In example 2, we can factor out 3xy out of each term. 3 is the GCF of 21, 6 and 3, and the lowest exponent we have of x and y is 1, so our GCF is 3xy.

 

21x³y - 6x²y⁴ + 3xy = 3xy(7x² - 2xy³ + 1)

 

So, now we have that over 3xy. What is 3xy/3xy? 1, because anything over itself is 1.

 

What are we left with? 7x² - 2xy³ + 1.

 

With example 1, what is the GCF of 2, -5, and -12? It's 1, so there is nothing to factor out. Because there is no m with -12, we can't factor out m to any power.

 

You can't just cancel separate terms. You can only cancel out factors.

 

Hope this helps!