Question

Which is the simplified form of 6 times x minus 18 all over 5 times x minus 15.?

negative 6 over 5.

x minus 3 over x minus 1.

3 over 5.

6 over 5.

Answer 1

Is A correct?

Answer 2

No.

Answer 3

I remember doing this a lot but I totally forgot the formula and I'm trying to figure it out lol.

Answer 4

Factor the numerator. Factor the denominator. What do you get?

Answer 5

B

Answer 6

Back to the old guessing game, eh?

Your life in math classes is going to be miserable if you don't learn how to do this.

Answer 7

Is there a common factor in the two terms in \[6x-18\]

Answer 8

2

Answer 9

What do you get if you divide both terms by 2?

Answer 10

18/2 = 6?

Answer 11

my bad. I meant 9

Answer 12

So that gives us \[2(3x-9)\]Are there any common factors in \(3x\) and \(9\)?

Answer 13

3?

Answer 14

You tell me :-)

Answer 15

3

Answer 16

So what do you get if you divide \(3x\) by \(3\)? How about \(9\) by \(3\)?

Answer 17

3x/3 is 1x. and 9/3=3

Answer 18

Excellent. So that means our numerator can be written as \[2*3(1x-3) = 6(x-3)\]

Now how about the denominator? \[5x-15\]See any common factors there?

Answer 19

5

Answer 20

Okay, if we factor out a 5, what do we have left?

Answer 21

1

Answer 22

No, I mean if we divide \[5x-15\]by \(5\), what do we get?

Answer 23

-2x

Answer 24

\[\frac{5x-15}5=\frac{5x}{5}-\frac{15}{5}=\]

Answer 25

I don't get that

Answer 26

Okay, what's \(5x\) divided by \(5\)?

Answer 27

1x

Answer 28

Right. and \(-15\) divided by \(5\)?

Answer 29

-3

Answer 30

Excellent. So that means we can rewrite \[5x-15\] as\[5(x-3)\]because \[5(x-3) = 5*x - 5*3 = 5x-15\]

So our fraction can be written
\[\frac{6(x-3)}{5(x-3)}\]Any ideas about how to simplify that sucker?

Answer 31

Umm... ughh... not too sure.

Answer 32

you can do this ^^ xD

Answer 33

Well, can't you cancel out the \(x-3\) terms, which appear on both the top and the bottom?

What's 3/3?

What's 5/5?

What's 235234/235234?

Aren't they all 1?

Answer 34

Yeah haha

Answer 35

As long as \(x\ne 3\), we can just cancel those two terms out:
\[\frac{6(x-3)}{5(x-3)} = \frac{6\cancel{(x-3)}}{5\cancel{(x-3)}} =\frac{6}{5}\]

Answer 36

\(x\) isn't allowed to be \(3\) in this fraction because that would involve dividing by \(0\), and that doesn't make any sense. Doesn't matter for this problem, though.

Answer 37

Awesome! Thanks!

Answer 38

So when you have to factor something like \(6x-18\), it's worth trying right off the bat dividing both numbers by the first number to see if works. If it does, that's much faster than dividing by 2, 3, etc.

Answer 39

I'll keep that in mind.

Answer 40

You can think of this factoring business as looking at a multi-car pileup and trying to figure out what the cars looked like before they collided :-)

Answer 41

Haha alright, thanks!

Answer 42

oh wow