Question

What is the solution to the equation 3/m+3- m/3-m=m^2+9/m^2-9?

Answer 1

AWNSER D. No solution

Answer 2

Answer: It has no solution.

Explanation:

Since we have given that

`(3)/(m+3)-(m)/(3-m)=(m^2+9)/(m^-9)`

We need to find the solution of the above equation:

since is a rational equation so, we will check for its extraneous solution.

`(3)/(m+3)-(m)/(3-m)=(m^2+9)/(m^-29)\\\\(3)/(m+3)+(m)/(m-3)=(m^2+9)/(m^2-9)\\\\(3(m-3)+m(m+3))/(m^2-9)=(m^2+9)/(m^2-9)\\\\(3m-9+m^2+3m)/(m^2-9)=(m^2+9)/(m^2-9)\\\\(m^2-9+6m)/(m^2-9)=(m^2+9)/(m^2-9)\\\\m^2+6m-9=m^2+9\\\\6m=18\\\\m=(18)/(6)=3`

Hence, the extraneous solution in case of rational equation is 3, when we put m=3, it becomes undefined so, it has no solution.