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

Question

asked Mar 10, 2021 90.9k views

1 Answer

Oleksandr · Answer 1 · 2021-03-14T12:18:13+0000

Answer:

$\displaystyle A=(x-2)/(x+3)$

$\displaystyle B=(-5)/((x+3)(x+2))$

Explanation:

We need to find two expressions with unlike denominators what sum

$\displaystyle S=(x-3)/(x+2)$

Let's suppose one of the expressions is:

$\displaystyle A=(x-2)/(x+3)$

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

$\displaystyle B=S-A=(x-3)/(x+2)-(x-2)/(x+3)$

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

$\displaystyle B=(x+3)(x-3)/((x+3)(x+2))-(x+2)(x-2)/((x+3)(x+2))$

Operating:

$\displaystyle B=(x^2-9)/((x+3)(x+2))-(x^2-4)/((x+3)(x+2))$

Subtracting both fractions with like denominators:

$\displaystyle B=(x^2-9-(x^2-4))/((x+3)(x+2))$

Simplifying:

$\displaystyle B=(-5)/((x+3)(x+2))$

Thus the two expressions are:

$\displaystyle A=(x-2)/(x+3)$

And

$\displaystyle B=(-5)/((x+3)(x+2))$