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

(1)/(x+9)+(7)/(x-8)=

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline1x+9+7x8= \frac{1}{x+9}+\frac{7}{x-8}=

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Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline1x+9+7x8= \frac{1}{x+9}+\frac{7}{x-8}=
  1. Identify Denominators: Identify the denominators of the two fractions. The first fraction has a denominator of (x+9)(x+9), and the second fraction has a denominator of (x8)(x-8).
  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 (x+9)(x8)(x+9)(x-8).
  3. Rewrite with Common Denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction becomes (1(x8))/((x+9)(x8))(1\cdot(x-8))/((x+9)(x-8)), and the second fraction becomes (7(x+9))/((x+9)(x8))(7\cdot(x+9))/((x+9)(x-8)).
  4. Expand Numerators: Expand the numerators of both fractions.\newlineFor the first fraction, the numerator becomes 1×x1×81\times x - 1\times 8, which simplifies to x8x - 8.\newlineFor the second fraction, the numerator becomes 7×x+7×97\times x + 7\times 9, which simplifies to 7x+637x + 63.
  5. Add Fractions with Common Denominator: Add the two fractions with the common denominator.\newlineThe sum of the fractions is (x8)+(7x+63)(x+9)(x8)\frac{(x - 8) + (7x + 63)}{(x+9)(x-8)}.
  6. Combine Like Terms: Combine like terms in the numerator.\newlineThe combined numerator is x8+7x+63x - 8 + 7x + 63, which simplifies to 8x+558x + 55.
  7. Final Simplified Expression: Write the final simplified expression.\newlineThe final simplified expression is (8x+55)/((x+9)(x8))(8x + 55)/((x+9)(x-8)).

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