Question

Add the rational expressions and simplify your answer

5/x+2 + 6/x−3=

Answer 1

To add the rational expressions \( \frac{5}{x+2} + \frac{6}{x-3} \), we need to find a common denominator. The common denominator in this case is \( (x + 2)(x - 3) \).

Now we can rewrite each fraction with the common denominator:

\[
\frac{5}{x+2} = \frac{5(x-3)}{(x+2)(x-3)}
\]
\[
\frac{6}{x-3} = \frac{6(x+2)}{(x-3)(x+2)}
\]

Now we can rewrite the entire expression:

\[
\frac{5(x-3)}{(x+2)(x-3)} + \frac{6(x+2)}{(x-3)(x+2)} = \frac{5(x-3) + 6(x+2)}{(x+2)(x-3)}
\]

Next, let's simplify the numerator:

\[
5(x-3) + 6(x+2) = 5x - 15 + 6x + 12 = 11x - 3
\]

Now our expression looks like this:

\[
\frac{11x - 3}{(x+2)(x-3)}
\]

Thus, the final simplified form of the expression is:

\[
\frac{11x - 3}{(x+2)(x-3)}
\]