Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−79+x3=□
Identify common denominator: Identify the common denominator for the two fractions.To add fractions, we need a common denominator. In this case, the denominators are (x−7) and x, so the common denominator will be the product of these two, which is x(x−7).
Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.We need to adjust the numerators to reflect the new common denominator.For the first fraction, (9)/(x−7), we multiply the numerator and denominator by x to get (9x)/(x(x−7)).For the second fraction, (3)/(x), we multiply the numerator and denominator by (x−7) to get (3(x−7))/(x(x−7)).
Combine fractions: Combine the fractions.Now that both fractions have the same denominator, we can combine them by adding their numerators.(x(x−7)9x)+(x(x−7)3(x−7))=x(x−7)9x+3(x−7)
Expand and simplify numerator: Expand and simplify the numerator.We distribute the 3 in the second term of the numerator.9x+3(x−7)=9x+3x−21Now, combine like terms.9x+3x−21=12x−21
Write final simplified expression: Write the final simplified expression.The combined fraction with the simplified numerator is:(12x−21)/(x(x−7))This is the simplified form of the sum of the two fractions.