Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−95+x−64=
Identify common denominator: Identify the common denominator for the fractions(5)/(x−9) and (4)/(x−6). To add fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x−9) and (x−6).
Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.The first fraction becomes (5)(x−6)/((x−9)(x−6)), and the second fraction becomes (4)(x−9)/((x−6)(x−9)).
Expand numerators: Expand the numerators of both fractions.For the first fraction, expand (5)(x−6) to get 5x−30.For the second fraction, expand (4)(x−9) to get 4x−36.
Combine numerators over common denominator: Combine the expanded numerators over the common denominator. The combined fraction is (5x−30+4x−36)/((x−9)(x−6)).
Simplify numerator: Simplify the numerator of the combined fraction.Add the like terms in the numerator: 5x+4x=9x and −30−36=−66.So, the simplified numerator is 9x−66.
Write simplified fraction: Write the simplified fraction.The simplified fraction is (9x−66)/((x−9)(x−6)).