Q. Subtract.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x+73−x−26=
Identify Common Denominator: Identify the common denominator for the two fractions.In order to subtract the fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x+7) and (x−2).Common Denominator: (x+7)(x−2)
Rewrite with Common Denominator: Rewrite each fraction with the common denominator.We need to adjust each fraction so that they both have the common denominator.(3)/(x+7) becomes (3)(x−2)/((x+7)(x−2))(6)/(x−2) becomes (6)(x+7)/((x+7)(x−2))
Expand Numerators: Expand the numerators of both fractions.Now we expand the numerators of both fractions.(3)(x−2)=3x−6(6)(x+7)=6x+42
Subtract Fractions: Subtract the second fraction from the first fraction.Now we subtract the second fraction from the first, keeping the common denominator.(3x−6)/((x+7)(x−2))−(6x+42)/((x+7)(x−2))
Combine Numerators: Combine the numerators over the common denominator. We combine the numerators into a single fraction over the common denominator. (3x−6−(6x+42))/((x+7)(x−2))
Simplify Numerator: Simplify the numerator.Now we simplify the numerator by distributing the negative sign and combining like terms.3x−6−6x−42=−3x−48
Write Simplified Fraction: Write the simplified fraction.The simplified fraction is now:(−3x−48)/((x+7)(x−2))