Respuesta :

I'm assuming the given expression is (x-3)/(x+2)

One way to break that down into the form A+B, where A and B are rational expressions, is to have
A = x/(x+2)
B = -3/(x+2)

The numerators x and -3 are added to get x-3 and the result is placed over the LCD (lowest common denominator)
facundo3141592

We want to come p with two expressions such that the sum is the given rational expression, the two expressions can be:

[tex]\frac{x}{x + 2} \\ \\ \frac{-3}{x + 2} [/tex]

How to find the expressions?

We want to find two expressions, that we can call f(x) and g(x) such that:

[tex]f(x) + g(x) = \frac{x - 3}{x + 2} [/tex]

So what we can try to do is to "break" the right part into two different parts, and each one of these will be an expression:

[tex]\frac{x - 3}{x + 2} = \frac{x}{x + 2} + \frac{-3}{x + 2} [/tex]

So the two expressions can be:

[tex]\frac{x}{x + 2} \\ \\ \frac{-3}{x + 2} [/tex]

If you want to learn more about rational expressions, you can read:

https://brainly.com/question/2670100

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