Q. Subtract.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x+38−x+82=
Identify common denominator: Identify the common denominator for the two fractions.To subtract the fractions, we need a common denominator. The common denominator for (x+3) and (x+8) is the product of the two, which is (x+3)(x+8).
Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.We need to express each fraction with the common denominator (x+3)(x+8). This means multiplying the numerator and denominator of each fraction by the necessary factor to achieve the common denominator.For the first fraction, x+38, we multiply the numerator and denominator by (x+8).For the second fraction, x+82, we multiply the numerator and denominator by (x+3).
Perform multiplication for each fraction: Perform the multiplication for each fraction.Now we multiply the numerators and denominators as determined in Step 2.First fraction: (8×(x+8))/((x+3)(x+8))Second fraction: (2×(x+3))/((x+3)(x+8))
Expand numerators: Expand the numerators.We need to expand the numerators of both fractions.First fraction's numerator: 8×(x+8)=8x+64Second fraction's numerator: 2×(x+3)=2x+6
Combine fractions by subtracting numerators: Combine the fractions by subtracting the numerators.Now that we have a common denominator, we can combine the fractions by subtracting the second fraction's numerator from the first fraction's numerator.(8x+64)−(2x+6)=8x+64−2x−6
Simplify the result: Simplify the result.Simplify the expression by combining like terms.8x+64−2x−6=(8x−2x)+(64−6)=6x+58
Write the final answer: Write the final answer.The final answer is the simplified numerator over the common denominator.(6x+58)/((x+3)(x+8))