Why

[bleak briar]

Uh

!original

[keen edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[bleak briar]

Ok, so we want a common denominator

[foggy otter]

The common denominator on the left side is x* (x+5x) * (x-5x), but I'm trying to figure out why not x(x+5x) * x(x-5x)

[bleak briar]

So we'd multiply the left fraction by (x - 5)/(x - 5) and the right fraction by (x + 5)/(x + 5)

[bleak briar]

x + 5 and x - 5 you mean, not x + 5x and x - 5x

Well, we already have x in common

So why multiply by another x?

[foggy otter]

ops, yes, x + 5 and x - 5

[bleak briar]

The left term and right term only don't have x + 5 and x - 5 in common, as you can see here

You could of course multiply the left term by x(x - 5) and the right term by x(x + 5), that'd work too

But it'd be unnecessary and you will have higher powers to work with

[foggy otter]

Why is this not necessary? I just don’t understand the logic why x* (x+5) * (x-5) is correct, and not x(x+5) * x(x-5)

[bleak briar]

Both are correct

And that's exactly why the second is unnecessary: with the first one, you only have degree 3 while with the second one, degree 4.

I will give you an analogous example:

[foggy otter]

Is it really possible in algebra to simply throw away the degree of a number?

[bleak briar]

Essentially this example has the same idea as what we are talking about right now

[bleak briar]

No. But what you are getting with x(x+5) * x(x-5) is not the least common multiple of the denominators

It's just a common multiple

[bleak briar]

I'd suggest really look at this example, it's basically the same principle