Amanda R. answered • 02/11/16
Tutor
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Math and Science by a certified TN teacher and homeschool mom
LCM means lowest common multiple. A multiple is any number/variable the starting number/variable can be divided into evenly. Common multiples are ones that two numbers/variables can divide into evenly.
the multiples of 2 are 2,4,6,8,10,12...
the multiples of 3 are 3,6,9,12...
there common multiples or 6,12,...
the LMC of 2 and 3 is 6
When working with larger numbers it can be easier to factor the larger number into smaller numbers
ex. LCM of 32 and 42
32=2 x 2 x 2 x 2 x 2
42=2 x 3 x 7
The factors of 32 and 42 have a 2 in common so our answer starts with 2 x ?.
Now that the we have accounted for the first 2 in each list we now need to include all of the other factors...
2 x 2 x 2 x 2 x 2
2 x 3 x 7
? = 2 x 2 x 2 x 2 x 3 x 7
The LCM will by 2 x 2 x 2 x 2 x 2 x 3 x 7= 672
the multiples of 2 are 2,4,6,8,10,12...
the multiples of 3 are 3,6,9,12...
there common multiples or 6,12,...
the LMC of 2 and 3 is 6
When working with larger numbers it can be easier to factor the larger number into smaller numbers
ex. LCM of 32 and 42
32=2 x 2 x 2 x 2 x 2
42=2 x 3 x 7
The factors of 32 and 42 have a 2 in common so our answer starts with 2 x ?.
Now that the we have accounted for the first 2 in each list we now need to include all of the other factors...
2 x 2 x 2 x 2 x 2
2 x 3 x 7
? = 2 x 2 x 2 x 2 x 3 x 7
The LCM will by 2 x 2 x 2 x 2 x 2 x 3 x 7= 672
Variables are just as easy
in your case you have x and x2. (x) can go directly into x2
The LCM will be x2
in your case you have x and x2. (x) can go directly into x2
The LCM will be x2
Amanda R.
Another tutor wrote out a step by step below. All I would add is to explain how he went from the initial problem to 2x-1=-3x2.
In order to get a fraction that equals 2/x but has x2 on the bottom you need to multiply 2/x by x/x. (Remember anything over itself in a fraction equals 1 and anything times 1 is still equal to itself)
2/x * x/x = 2x/x2
(2x/x2) - (1/x2) = -3
(2x-1)/x2 = -3
We don't want a variable we are trying to solve for to be on the bottom of a fraction so we always want to address that first. That is why Arthur (answer below) multiplied both sides by x2.
x2 * [(2x-1)/x2] = -3 * x2
On the left side the x2 cancel each other out and you end up with...
2x-1=-3x2
You can follow the rest in the answer below.
Note there are 2 answers because if x makes either (3x-1) or (x+1) equal to zero then the answer will be zero since anything times zero = zero.
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02/11/16
Taylor G.
02/11/16