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Add.
The numerator should be expanded and simplified. The denominator should be either expanded or factored.

(2)/(x-3)+(5)/(x+1)=

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline2x3+5x+1= \frac{2}{x-3}+\frac{5}{x+1}=

Full solution

Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline2x3+5x+1= \frac{2}{x-3}+\frac{5}{x+1}=
  1. Find common denominator: To add the two fractions, we need a common denominator. The common denominator for (x3)(x-3) and (x+1)(x+1) is the product of the two, which is (x3)(x+1)(x-3)(x+1).
  2. Rewrite fractions with common denominator: We will rewrite each fraction with the common denominator. For the first fraction, we multiply the numerator and denominator by (x+1)(x+1), and for the second fraction, we multiply the numerator and denominator by (x3)(x-3).
  3. Expand the numerators: After rewriting, we have: 2(x+1)(x3)(x+1)+5(x3)(x3)(x+1)\frac{2 \cdot (x+1)}{(x-3)(x+1)} + \frac{5 \cdot (x-3)}{(x-3)(x+1)}
  4. Combine numerators over common denominator: Now we expand the numerators:\newline(2x+2)/((x3)(x+1))+(5x15)/((x3)(x+1))(2x + 2) / ((x-3)(x+1)) + (5x - 15) / ((x-3)(x+1))
  5. Simplify the numerator: Next, we combine the numerators over the common denominator: \newlineegin{equation}\newline\frac{22x + 22 + 55x - 1515}{(x3-3)(x+11)}\newline\end{equation}
  6. No further simplification possible: We simplify the numerator by combining like terms: \newlineegin{equation}\newline\frac{77x - 1313}{(x3-3)(x+11)}\newline\end{equation}
  7. No further simplification possible: We simplify the numerator by combining like terms: \newline(7x13)/((x3)(x+1))(7x - 13) / ((x-3)(x+1))The expression is now simplified, and there is no further simplification possible for the denominator since it is already factored and does not have common factors with the numerator.