If when simplifying 2 rational expressions you got:
(-2(x-3))/2-x
would you multiply the top & bottom by -1?
Thanks!! :)♡
I assume the denominator is (2-x).
If so, you can, it makes it neater
(2(x-3))/(x-2)
Is it necessary? I bet I could find a few middle/high school teachers who would vehemently argue so. If you have one of those, dont argue, just say thanks, I didn't know that. It is not worth arguing.
Math is a language, with a living syntax, and that syntax changes over time...how we express algebraic terms and statements can vary.
The most important thing in your statement above was the parenthesis on the denominator (2-x), that is important.
Ok, that makes sense :) thank you very much
To simplify the expression (-2(x-3))/2-x, you can start by distributing the -2 to the terms inside the parentheses:
(-2(x-3))/2 - x
= (-2x + 6)/2 - x
Now, you need to find a common denominator for the fractions. The common denominator here is 2 because both fractions have it as their denominator. To add or subtract fractions, they must have the same denominator.
So, let's rewrite the expression with a common denominator of 2:
[(-2x + 6) - 2(x)]/2
= (-2x + 6 - 2x)/2
= (-4x + 6)/2
= -2x + 3
Therefore, the simplified form of (-2(x-3))/2-x is -2x + 3.
To answer your question, multiplying the top and bottom of a rational expression by -1 is a valid step if you want to rewrite the expression with a positive denominator. However, in this particular case, it is not necessary as the - sign does not affect the simplification process.