Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x+91+x−87=
Identify Denominators: Identify the denominators of the two fractions. The first fraction has a denominator of (x+9), and the second fraction has a denominator of (x−8).
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+9)(x−8).
Rewrite with Common Denominator: Rewrite each fraction with the common denominator.The first fraction becomes (1⋅(x−8))/((x+9)(x−8)), and the second fraction becomes (7⋅(x+9))/((x+9)(x−8)).
Expand Numerators: Expand the numerators of both fractions.For the first fraction, the numerator becomes 1×x−1×8, which simplifies to x−8.For the second fraction, the numerator becomes 7×x+7×9, which simplifies to 7x+63.
Add Fractions with Common Denominator: Add the two fractions with the common denominator.The sum of the fractions is (x+9)(x−8)(x−8)+(7x+63).
Combine Like Terms: Combine like terms in the numerator.The combined numerator is x−8+7x+63, which simplifies to 8x+55.
Final Simplified Expression: Write the final simplified expression.The final simplified expression is (8x+55)/((x+9)(x−8)).