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

(5)/(x-6)-(1)/(x+5)=

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline5x61x+5= \frac{5}{x-6}-\frac{1}{x+5}=

Full solution

Q. Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline5x61x+5= \frac{5}{x-6}-\frac{1}{x+5}=
  1. Identify Common Denominator: Identify the common denominator for the two fractions.\newlineTo subtract the fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x6)(x-6) and (x+5)(x+5).\newlineCommon Denominator: (x6)(x+5)(x-6)(x+5)
  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.\newlineFor the first fraction, (5)/(x6)(5)/(x-6), we multiply the numerator and denominator by (x+5)(x+5).\newlineFor the second fraction, (1)/(x+5)(1)/(x+5), we multiply the numerator and denominator by (x6)(x-6).\newlineAdjusted Fractions: 5(x+5)(x6)(x+5)1(x6)(x6)(x+5)\frac{5(x+5)}{(x-6)(x+5)} - \frac{1(x-6)}{(x-6)(x+5)}
  3. Expand Numerators: Expand the numerators of the adjusted fractions.\newlineNow we expand the numerators of both fractions.\newlineFirst Fraction: 5(x+5)=5x+255(x+5) = 5x + 25\newlineSecond Fraction: 1(x6)=x61(x-6) = x - 6\newlineExpanded Numerators: (5x+25)(x6)(5x + 25) - (x - 6)
  4. Combine Numerators: Combine the numerators over the common denominator.\newlineNow we combine the expanded numerators over the common denominator.\newlineCombined Fraction: (5x+25)(x6)(x6)(x+5)\frac{(5x + 25) - (x - 6)}{(x-6)(x+5)}
  5. Simplify Numerator: Simplify the numerator.\newlineWe need to subtract the second numerator from the first.\newlineSimplified Numerator: (5x+25)(x6)=5x+25x+6(5x + 25) - (x - 6) = 5x + 25 - x + 6\newlineSimplified Numerator: 4x+314x + 31
  6. Write Final Expression: Write the final simplified expression.\newlineThe final simplified expression is the simplified numerator over the common denominator.\newlineFinal Expression: (4x+31)/((x6)(x+5))(4x + 31)/((x-6)(x+5))

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