Question

Write two expressions with unlike denominators whose sum is x-3/x+2, I need help it is confusing for me.

Answer 1

Answer:

$\displaystyle A=\frac{x-2}{x+3}$

$\displaystyle B=\frac{-5}{(x+3)(x+2)}$

Step-by-step explanation:

We need to find two expressions with unlike denominators what sum

$\displaystyle S=\frac{x-3}{x+2}$

Let's suppose one of the expressions is:

$\displaystyle A=\frac{x-2}{x+3}$

Now we subtract S minus A to find the other expression B:

$\displaystyle B=S-A=\frac{x-3}{x+2}-\frac{x-2}{x+3}$

Multiply the first fraction by x+3 and the second by x+2;

$\displaystyle B=(x+3)\frac{x-3}{(x+3)(x+2)}-(x+2)\frac{x-2}{(x+3)(x+2)}$

Operating:

$\displaystyle B=\frac{x^2-9}{(x+3)(x+2)}-\frac{x^2-4}{(x+3)(x+2)}$

Subtracting both fractions with like denominators:

$\displaystyle B=\frac{x^2-9-(x^2-4)}{(x+3)(x+2)}$

Simplifying:

$\displaystyle B=\frac{-5}{(x+3)(x+2)}$

Thus the two expressions are:

$\displaystyle A=\frac{x-2}{x+3}$

And

$\displaystyle B=\frac{-5}{(x+3)(x+2)}$