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

(9)/(x-7)+(3)/(x)=◻

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline9x7+3x= \frac{9}{x-7}+\frac{3}{x}=\square

Full solution

Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline9x7+3x= \frac{9}{x-7}+\frac{3}{x}=\square
  1. Identify common denominator: Identify the common denominator for the two fractions.\newlineTo add fractions, we need a common denominator. In this case, the denominators are (x7)(x-7) and xx, so the common denominator will be the product of these two, which is x(x7)x(x-7).
  2. Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.\newlineWe need to adjust the numerators to reflect the new common denominator.\newlineFor the first fraction, (9)/(x7)(9)/(x-7), we multiply the numerator and denominator by xx to get (9x)/(x(x7))(9x)/(x(x-7)).\newlineFor the second fraction, (3)/(x)(3)/(x), we multiply the numerator and denominator by (x7)(x-7) to get (3(x7))/(x(x7))(3(x-7))/(x(x-7)).
  3. Combine fractions: Combine the fractions.\newlineNow that both fractions have the same denominator, we can combine them by adding their numerators.\newline(9xx(x7))+(3(x7)x(x7))=9x+3(x7)x(x7)(\frac{9x}{x(x-7)}) + (\frac{3(x-7)}{x(x-7)}) = \frac{9x + 3(x-7)}{x(x-7)}
  4. Expand and simplify numerator: Expand and simplify the numerator.\newlineWe distribute the 33 in the second term of the numerator.\newline9x+3(x7)=9x+3x219x + 3(x-7) = 9x + 3x - 21\newlineNow, combine like terms.\newline9x+3x21=12x219x + 3x - 21 = 12x - 21
  5. Write final simplified expression: Write the final simplified expression.\newlineThe combined fraction with the simplified numerator is:\newline(12x21)/(x(x7))(12x - 21)/(x(x-7))\newlineThis is the simplified form of the sum of the two fractions.

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