Question

Simplify the rational expression: (5m + 40)/(m + 8).

a) (5m + 40)/(m + 8)
b) 5m + 40
c) 5m - 5
d) 5m

Answer 1

To simplify the expression (5m + 40)/(m + 8), factor out the common divisor of 5, which gives 5(m + 8)/(m + 8), and then eliminate the common term (m + 8), leaving the simplified expression as 5.

Step-by-step explanation:

To simplify the rational expression (5m + 40)/(m + 8), we look for any common factors in the numerator and the denominator. Notice that the term 40 is a multiple of 8, so we can factor out the greatest common factor of 5 from the numerator. The simplified expression would then be just 5, since 5m/ m is 5 and 40/8 is also 5.

The step-by-step explanation is as follows:

1. Factor out the greatest common divisor (5) in the numerator: (5m + 40) = 5(m + 8).
2. Divide by the common factor in the denominator: (m + 8).
3. Eliminate the common term (m + 8) in both numerator and denominator.

So the simplified expression is 5.

It is important to eliminate terms wherever possible to simplify the algebra and to always check the answer to see if it is reasonable.