Q. Subtract.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−41−x+65=
Identify common denominator: Identify the common denominator for the two fractions.The common denominator for the fractions (1)/(x−4) and (5)/(x+6) is the product of the two distinct denominators, which is (x−4)(x+6).
Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.To subtract the fractions, they must have the same denominator. We rewrite each fraction as follows:(1)/(x−4) becomes (1∗(x+6))/((x−4)(x+6))(5)/(x+6) becomes (5∗(x−4))/((x−4)(x+6))
Expand numerators: Expand the numerators of both fractions.Now we expand the numerators:For (1∗(x+6))/((x−4)(x+6)), the numerator is x+6.For (5∗(x−4))/((x−4)(x+6)), the numerator is 5x−20.
Subtract second fraction: Subtract the second fraction from the first fraction.Now we subtract the second fraction from the first, keeping the common denominator:(x−4)(x+6)(x+6)−(5x−20)
Combine like terms in numerator: Combine like terms in the numerator.Now we combine like terms in the numerator:(x+6)−(5x−20)=x+6−5x+20=−4x+26
Write final simplified form: Write the final simplified form of the expression.The final simplified form of the expression is:(−4x+26)/((x−4)(x+6))