Help with rational expressions

Ana Ng

I'm working on notes for an upcoming math exam, and right now going over some rational expressions. I'm getting tripped up on simplifying to lowest terms on some of them, and hopefully it's something small and silly that I'm just overlooking!

There are two problems I'm working on, first is:

6m + 18
7m + 21

Back of the book says the answer is 6/7. I'm confused because I don't understand what happened to the m part of this expression. When I first looked at it I expected the answer to be 6m + 6 over 7m + 7.

The second problem is

3z^2 + z
18z + 6

The book is saying the answer is z/6, so I tried to work backwards figuring out how to factor and rewrite to cancel enough things out to get down to z/6, so I ended up with
z(z+3) + z
6(z+3) + 6

So the z+3 cancels each other out, but that would leave me with z+z over 6+6 which is obviously not correct so I know that I'm doing something wrong somewhere.

zerzhul

for the first one, you can pull out a factor of (6/7) to get

6(m + 3)
7(m + 3)

this reduces to 6/7

zerzhul

in the second

3z^2 + z
18z + 6

z(3z + 1)
6(3z + 1)

this reduces to z/6

zerzhul

Basically you're just looking for common factors to remove.

For the first, the common thing in the numerator is the 6, in the denominator, the 7. Factoring those out reveals the canceled terms.

For the second, the common thing on the top is "z", the denominator, the common thing is the 6.

k-maps

for the second one:

you can factor to:

z(3z + 1)
6(3z+1)

you just confused the factorization of z with the constant.

Ana Ng

blurgh, yup that makes much more sense and makes me feel pretty dumb :P

thanks for the help - I think this can probably be closed now!

djmitchella

Second one, you're close, but the factor is 3z+1, not 1z + 3; then you get:

z*(3z+1)
6*(3z+1)

=

z*3z + z*1
6*3z + 6*1

=

3z^2 + z
18z + 6

which is what you're after.