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

(7)/(x)-(2)/(x+8)=◻

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline7x2x+8= \frac{7}{x}-\frac{2}{x+8}=\square

Full solution

Q. Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline7x2x+8= \frac{7}{x}-\frac{2}{x+8}=\square
  1. Identify common denominator: Identify a common denominator for the two fractions.\newlineSince the denominators are xx and x+8x+8, the common denominator will be x(x+8)x(x+8).
  2. Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.\newlineThe first fraction becomes (7x(x+8))/(x(x+8))(7x(x+8))/(x(x+8)) and the second fraction becomes (2x(x+8))/(x(x+8))(2x(x+8))/(x(x+8)).
  3. Expand numerators: Expand the numerators of both fractions.\newlineFor the first fraction, the numerator is 77 and does not need expansion. For the second fraction, the numerator is 2(x+8)2(x+8), which expands to 2x+162x + 16.
  4. Combine fractions: Combine the fractions by subtracting the numerators and keeping the common denominator.\newlineThe combined fraction is (7(2x+16))/(x(x+8))(7 - (2x + 16))/(x(x+8)).
  5. Simplify numerator: Simplify the numerator of the combined fraction. Simplify 7(2x+16)7 - (2x + 16) to 72x167 - 2x - 16.
  6. Combine like terms: Continue simplifying the numerator by combining like terms. Combine 77 and 16-16 to get 9-9, so the numerator becomes 2x9-2x - 9.
  7. Write final simplified fraction: Write the final simplified fraction.\newlineThe final answer is (2x9)/(x(x+8))(-2x - 9)/(x(x+8)).