Question

I am confused on finding the least common denominator for polynomails

Answer 1

\[\frac{ 4x }{3x-4 }+\frac{ 8 }{ 3x ^{2}-4x }+\frac{ 2 }{ x }\] I know it is (3x-4) but I do not know how to know which is the least for when I look at a problem.

Answer 2

can the middle denominator be factored?

Answer 3

yes

Answer 4

then id go ahead and factor it, it easiest to see when they are all in factored forms

Answer 5

x(3x-4)

Answer 6

now we look at "parts" to see what each one is missing

Answer 7

to make it equal to the middles original formula? 3x^2-4x

Answer 8

now we look at "parts" to see what each one is missing

Answer 9

ugh ... latex coding made my browser crash ....

Answer 10

4x 8 2
----- + ------- + ----
(3x-4) x(3x-4) x
^^^ ^^
needs an x needs an (3x-4)

Answer 11

4xx 8 2(3x-4)
------- + ------- + --------
x(3x-4) x(3x-4) x(3x-4)



4x^2 + 8+ 2(3x-4)
--------------------
x(3x-4)

Answer 12

oh ok then the top would be \[4x(x) + 8 (since the formula below was complete) + 2(3x-4)\]

Answer 13

now what if the problem includes a denominator that can not be factored?

Answer 14

then you simply use it as one of the parts ...

Answer 15

the idea is to make sure all the denominators have the same parts in the end

Answer 16

oh ok thank you very much, this teacher does not show steps so helped alot on explaining them. Thank you again.

Answer 17

the higher you get in math classes, the more they expect you to have learned prior ;)