Question

Please help? Add or subtract the rational expressions. Simplify Answeres if possible

Answer 1

1) `6/(a+3)`
2) `x-4`

Explanation:

Luckily, both of the problems have two fractions with the same denominator. All we have to do to simplify is to combine the fractions. Think of it this way:

`a/b+c/b = (a+c)/b` and `a/b-c/b = (a-c)/b`

Let's use this to solve these two problems:

1)`2/(a+3)+4/(a+3) = (2+4)/(a+3) = 6/(a+3)`

We can't simplify this any further because there is no common factor we can divide each of the terms by.

For our next problem, though, we must combine our fractions, then factor and cancel out binomials to completely simplify:

2)`x^2/(x-2)-(6x-8)/(x-2) = (x^2-(6x-8))/(x-2) = (x^2-6x+8)/(x-2)`

Next, let's factor our trinomial in the numerator. `(x-4)(x-2) = x^2-2x-4x+8 = x^2-6x+8`, so we now have:

`((x-4)(x-2))/(x-2)`

We can now cancel out `(x-2)`, which leaves us with:

`((x-4)(cancel(x-2)))/(cancel(x-2)) = x-4`