Another algebra question?

Question

10x-(10/x^2) = 112 + 2/3

I posted this in question before and was told to multiply everything by 3x^2. I see the reasoning behind doing this, but how do you determine that 3x^2 was the right number for doing it? I'm sure it just wasn't a guess?

Answer 1

this equation contains fractions, so to make it easier to deal with, you can remove the fractions by multiplying the entire equation by the common denominator. here the common denominator is 3x^2. to find the common denominators, just multiply all the bottom numbers.

Answer 2

When you deal with equations that involve fractions, the first thing you try to do is to remove fractions. On the left, you see the denominator is x^2. Therefore, if you multiply both sides by x^2, your left side will be "fraction less." Now, you have to do the same thing to the right side. You see the denominator is 3. Multiply both sides AGAIN by 3 to remove the fractions on the left side.

That is the same thing as multiplying both sides by 3x^2.

This way, you only do this once, not once for the left side and one more time for the right side.

It is up to you if you want to do it all at once or one side at a time. Either way, you will end up with the same result. I would suggest you do it one side at a time, until you get used to the idea of removing fractions.

Answer 3

Multiplying by 3x^2 ensures that you have no denominators in any of your terms. This makes the algebra much simpler to manage.

Since x^2 is the denominator in the second term to the left of the equal sign, and 3 is the denominator in the second term to the right of the equal sign, multiplying by 3x^2 will ensure that none of your terms will have a denominator.

Answer 4

solve 10x-(10/x^2) = 112 + 2/3:

10x - (10/x^2) ----> (10x^3 - 10)/(x^2)
112 + (2/3) ----> 338 / 3

(10x^3 - 10)/(x^2) = 338 / 3

you can see that the denominators are (x^2) and 3

giving you 3x^2..