Q. Subtract.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x+28−x+56=
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+2) and (x+5).
Rewrite with Common Denominator: Rewrite each fraction with the common denominator.The first fraction becomes (8)(x+5)/[(x+2)(x+5)] and the second fraction becomes (6)(x+2)/[(x+2)(x+5)].
Expand Numerators: Expand the numerators of both fractions. Expand (8)(x+5) to get 8x+40 and (6)(x+2) to get 6x+12.
Subtract Fractions: Subtract the second fraction from the first fraction.Now we have (8x+40)/[(x+2)(x+5)]−(6x+12)/[(x+2)(x+5)].
Combine Numerators: Combine the numerators over the common denominator. Combine the numerators by subtracting the second from the first to get (8x+40−6x−12)/[(x+2)(x+5)].
Simplify Numerator: Simplify the numerator.Simplify 8x+40−6x−12 to get 2x+28.
Final Simplified Expression: Write the final simplified expression.The final simplified expression is (2x+28)/[(x+2)(x+5)].