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

(3)/(x+7)-(6)/(x-2)=

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline3x+76x2= \frac{3}{x+7}-\frac{6}{x-2}=

Full solution

Q. Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline3x+76x2= \frac{3}{x+7}-\frac{6}{x-2}=
  1. Identify Common Denominator: Identify the common denominator for the two fractions.\newlineIn order to subtract the fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x+7)(x+7) and (x2)(x-2).\newlineCommon Denominator: (x+7)(x2)(x+7)(x-2)
  2. Rewrite with Common Denominator: Rewrite each fraction with the common denominator.\newlineWe need to adjust each fraction so that they both have the common denominator.\newline(3)/(x+7)(3)/(x+7) becomes (3)(x2)/((x+7)(x2))(3)(x-2)/((x+7)(x-2))\newline(6)/(x2)(6)/(x-2) becomes (6)(x+7)/((x+7)(x2))(6)(x+7)/((x+7)(x-2))
  3. Expand Numerators: Expand the numerators of both fractions.\newlineNow we expand the numerators of both fractions.\newline(3)(x2)=3x6(3)(x-2) = 3x - 6\newline(6)(x+7)=6x+42(6)(x+7) = 6x + 42
  4. Subtract Fractions: Subtract the second fraction from the first fraction.\newlineNow we subtract the second fraction from the first, keeping the common denominator.\newline(3x6)/((x+7)(x2))(6x+42)/((x+7)(x2))(3x - 6)/((x+7)(x-2)) - (6x + 42)/((x+7)(x-2))
  5. Combine Numerators: Combine the numerators over the common denominator. We combine the numerators into a single fraction over the common denominator. (3x6(6x+42))/((x+7)(x2))(3x - 6 - (6x + 42))/((x+7)(x-2))
  6. Simplify Numerator: Simplify the numerator.\newlineNow we simplify the numerator by distributing the negative sign and combining like terms.\newline3x66x42=3x483x - 6 - 6x - 42 = -3x - 48
  7. Write Simplified Fraction: Write the simplified fraction.\newlineThe simplified fraction is now:\newline(3x48)/((x+7)(x2))(-3x - 48)/((x+7)(x-2))

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