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

(5)/(x-9)+(4)/(x-6)=

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline5x9+4x6= \frac{5}{x-9}+\frac{4}{x-6}=

Full solution

Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline5x9+4x6= \frac{5}{x-9}+\frac{4}{x-6}=
  1. Identify common denominator: Identify the common denominator for the fractions (5)/(x9)(5)/(x-9) and (4)/(x6)(4)/(x-6). To add fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x9)(x-9) and (x6)(x-6).
  2. Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction becomes (5)(x6)/((x9)(x6))(5)(x-6)/((x-9)(x-6)), and the second fraction becomes (4)(x9)/((x6)(x9))(4)(x-9)/((x-6)(x-9)).
  3. Expand numerators: Expand the numerators of both fractions.\newlineFor the first fraction, expand (5)(x6)(5)(x-6) to get 5x305x - 30.\newlineFor the second fraction, expand (4)(x9)(4)(x-9) to get 4x364x - 36.
  4. Combine numerators over common denominator: Combine the expanded numerators over the common denominator. The combined fraction is (5x30+4x36)/((x9)(x6))(5x - 30 + 4x - 36)/((x-9)(x-6)).
  5. Simplify numerator: Simplify the numerator of the combined fraction.\newlineAdd the like terms in the numerator: 5x+4x=9x5x + 4x = 9x and 3036=66-30 - 36 = -66.\newlineSo, the simplified numerator is 9x669x - 66.
  6. Write simplified fraction: Write the simplified fraction.\newlineThe simplified fraction is (9x66)/((x9)(x6))(9x - 66)/((x-9)(x-6)).

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