Question

The simplest form of the expression 4m-17/m^2-16 + 3m-11/m^2-16 has ____in the numerator and___ in the denominator.

Answer 1

For this case we have the following expression:
 $\frac{4m-17}{m^2-16} + \frac{3m-11}{m^2-16}$
 Since the denominator is equal, then we can add the numerator.
 We have then:
 $\frac{(4m-17) + (3m-11)}{m^2-16}$
 Adding similar terms we have:
 $\frac{(4m+3m) + (-17-11)}{m^2-16}$
 Rewriting we have:
 $\frac{7m - 28}{m^2-16}$
 Doing common factor in the numerator we have:
 $\frac{7(m - 4)}{m^2-16}$
 Factoring the denominator we have:
 $\frac{7(m - 4)}{(m-4)(m+4)}$
 Canceling similar terms we have:
 $\frac{7}{m+4}$
 Answer:
 The simplest form of the expression has 7 in the numerator and m+4 in the denominator.