How is doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions?

I'm not sure if this is exactly the answer you're looking for, but I know multiplying something by 1/2 is the same as dividing it by 2. I hope I helped!

Doing operations with rational expressions is very similar to doing operations with fractions because rational expressions are essentially fractions with variables in them. Both involve adding, subtracting, multiplying, and dividing.

To add or subtract rational expressions, you need to have a common denominator, just like with fractions. To find a common denominator, you first find the least common multiple (LCM) of the denominators, and then rewrite each rational expression with the common denominator. Finally, you can combine the numerators and simplify if necessary.

To multiply rational expressions, you simply multiply the numerators together and the denominators together. It is important to simplify the resulting expression by canceling out any common factors.

Dividing rational expressions is similar to multiplying, but with a twist. Instead of dividing directly, you need to multiply by the reciprocal of the second rational expression. This involves flipping the second rational expression and then using the same steps as multiplication.

It is worth noting that when dealing with expressions that include variables, it is often recommended to simplify as much as possible and check for any restrictions on the variables before performing any operations. This helps avoid divisions by zero or undefined values.