Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−42+x+39=
Identify Denominators: Identify the denominators of the two fractions.The first fraction has a denominator of (x−4), and the second fraction has a denominator of (x+3).
Find Common Denominator: Find a common denominator for the two fractions.The common denominator will be the product of the two distinct denominators, which is (x−4)(x+3).
Rewrite with Common Denominator: Rewrite each fraction with the common denominator.The first fraction becomes (2)(x+3)/[(x−4)(x+3)], and the second fraction becomes (9)(x−4)/[(x−4)(x+3)].
Expand Numerators: Expand the numerators of both fractions.For the first fraction, expand (2)(x+3) to get 2x+6.For the second fraction, expand (9)(x−4) to get 9x−36.
Combine over Common Denominator: Combine the expanded numerators over the common denominator. The combined fraction is (2x+6+9x−36)/[(x−4)(x+3)].
Simplify Numerator: Simplify the numerator of the combined fraction. Add the like terms in the numerator to get (2x+9x)+(6−36), which simplifies to 11x−30.
Write Simplified Fraction: Write the simplified fraction.The simplified fraction is (11x−30)/[(x−4)(x+3)].