Q. Subtract.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−65−x+51=
Identify Common Denominator: Identify the common denominator for the two fractions.To subtract the fractions, we need a common denominator. The common denominator will be the product of the two distinct denominators (x−6) and (x+5).Common Denominator: (x−6)(x+5)
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.For the first fraction, (5)/(x−6), we multiply the numerator and denominator by (x+5).For the second fraction, (1)/(x+5), we multiply the numerator and denominator by (x−6).Adjusted Fractions: (x−6)(x+5)5(x+5)−(x−6)(x+5)1(x−6)
Expand Numerators: Expand the numerators of the adjusted fractions.Now we expand the numerators of both fractions.First Fraction: 5(x+5)=5x+25Second Fraction: 1(x−6)=x−6Expanded Numerators: (5x+25)−(x−6)
Combine Numerators: Combine the numerators over the common denominator.Now we combine the expanded numerators over the common denominator.Combined Fraction: (x−6)(x+5)(5x+25)−(x−6)
Simplify Numerator: Simplify the numerator.We need to subtract the second numerator from the first.Simplified Numerator: (5x+25)−(x−6)=5x+25−x+6Simplified Numerator: 4x+31
Write Final Expression: Write the final simplified expression.The final simplified expression is the simplified numerator over the common denominator.Final Expression: (4x+31)/((x−6)(x+5))