Final answer:
The missing numerator that makes the fractions equivalent is the expression (-7m^2 + 21m). This is obtained by ensuring that the terms cancel correctly when the fractions are simplified.
Step-by-step explanation:
The question is to find the missing numerator that would make the two given fractions equivalent:
(-7m)/(m+5) = (?) / (m(m-3)(m+5))
To make the fractions equivalent, we need to find a numerator that when placed over the common denominator (m(m-3)(m+5)) will simplify to (-7m)/(m+5). We notice that the denominator of the second fraction already has (m+5) in it, which is the same as the denominator of the first fraction. Therefore, the missing numerator must contain the factor that will cancel out this common term when simplified.
Let's denote the missing numerator as X. To solve for X, we cross-multiply:
X × (m+5) = -7m × (m(m-3))
By expanding the right side, we get:
-7m^2 + 21m
This expanded expression is the missing numerator X that makes the given fractions equivalent when simplified.