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

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

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline1x45x+6= \frac{1}{x-4}-\frac{5}{x+6}=

Full solution

Q. Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline1x45x+6= \frac{1}{x-4}-\frac{5}{x+6}=
  1. Identify common denominator: Identify the common denominator for the two fractions.\newlineThe common denominator for the fractions (1)/(x4)(1)/(x-4) and (5)/(x+6)(5)/(x+6) is the product of the two distinct denominators, which is (x4)(x+6)(x-4)(x+6).
  2. Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.\newlineTo subtract the fractions, they must have the same denominator. We rewrite each fraction as follows:\newline(1)/(x4)(1)/(x-4) becomes (1(x+6))/((x4)(x+6))(1*(x+6))/((x-4)(x+6))\newline(5)/(x+6)(5)/(x+6) becomes (5(x4))/((x4)(x+6))(5*(x-4))/((x-4)(x+6))
  3. Expand numerators: Expand the numerators of both fractions.\newlineNow we expand the numerators:\newlineFor (1(x+6))/((x4)(x+6))(1*(x+6))/((x-4)(x+6)), the numerator is x+6x+6.\newlineFor (5(x4))/((x4)(x+6))(5*(x-4))/((x-4)(x+6)), the numerator is 5x205x-20.
  4. Subtract second fraction: Subtract the second fraction from the first fraction.\newlineNow we subtract the second fraction from the first, keeping the common denominator:\newline(x+6)(5x20)(x4)(x+6)\frac{(x+6)-(5x-20)}{(x-4)(x+6)}
  5. Combine like terms in numerator: Combine like terms in the numerator.\newlineNow we combine like terms in the numerator:\newline(x+6)(5x20)=x+65x+20=4x+26(x+6)-(5x-20) = x+6-5x+20 = -4x+26
  6. Write final simplified form: Write the final simplified form of the expression.\newlineThe final simplified form of the expression is:\newline(4x+26)/((x4)(x+6))(-4x+26)/((x-4)(x+6))

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