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:

`(4m-17)/(m^2-16) + (3m-11)/(m^2-16)`
Since the denominator is equal, then we can add the numerator.
We have then:

`((4m-17) + (3m-11))/(m^2-16)`
Adding similar terms we have:

`((4m+3m) + (-17-11))/(m^2-16)`
Rewriting we have:

`(7m - 28)/(m^2-16)`
Doing common factor in the numerator we have:

`(7(m - 4))/(m^2-16)`
Factoring the denominator we have:

`(7(m - 4))/((m-4)(m+4))`
Canceling similar terms we have:

`(7)/(m+4)`
Answer:
The simplest form of the expression has 7 in the numerator and m+4 in the denominator.