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

(2)/(x-4)+(9)/(x+3)=

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline2x4+9x+3= \frac{2}{x-4}+\frac{9}{x+3}=

Full solution

Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline2x4+9x+3= \frac{2}{x-4}+\frac{9}{x+3}=
  1. Identify Denominators: Identify the denominators of the two fractions.\newlineThe first fraction has a denominator of (x4)(x-4), and the second fraction has a denominator of (x+3)(x+3).
  2. Find Common Denominator: Find a common denominator for the two fractions.\newlineThe common denominator will be the product of the two distinct denominators, which is (x4)(x+3)(x-4)(x+3).
  3. Rewrite with Common Denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction becomes (2)(x+3)/[(x4)(x+3)](2)(x+3)/[(x-4)(x+3)], and the second fraction becomes (9)(x4)/[(x4)(x+3)](9)(x-4)/[(x-4)(x+3)].
  4. Expand Numerators: Expand the numerators of both fractions.\newlineFor the first fraction, expand (2)(x+3)(2)(x+3) to get 2x+62x + 6.\newlineFor the second fraction, expand (9)(x4)(9)(x-4) to get 9x369x - 36.
  5. Combine over Common Denominator: Combine the expanded numerators over the common denominator. The combined fraction is (2x+6+9x36)/[(x4)(x+3)](2x + 6 + 9x - 36)/[(x-4)(x+3)].
  6. Simplify Numerator: Simplify the numerator of the combined fraction. Add the like terms in the numerator to get (2x+9x)+(636)(2x + 9x) + (6 - 36), which simplifies to 11x3011x - 30.
  7. Write Simplified Fraction: Write the simplified fraction.\newlineThe simplified fraction is (11x30)/[(x4)(x+3)](11x - 30)/[(x-4)(x+3)].

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