Question

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

Om=3
m=6
all real numbers
no solution

Answer 1

no solution

Explanation:

If we subtract the left side of the equation, we get ...

`(m^2+9)/(m^2-9)-(3)/(m+3)+(3)/(3-m)=0\\\\(m^2+9-3(m-3)-3(m+3))/((m-3)(m+3))=0\\\\(m^2-6m+9)/((m-3)(m+3))=0=((m-3)^2)/((m-3)(m+3))\\\\(m-3)/(m+3)=0\quad\text{m$\\e$3}`

This equation will equal zero only if m=3, which is disallowed because it makes the denominator zero. Thus, there is no solution.