Question

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

Answer 1

Answer:

  no solution

Step-by-step explanation:

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

  $\dfrac{m^2+9}{m^2-9}-\dfrac{3}{m+3}+\dfrac{3}{3-m}=0\\\\\dfrac{m^2+9-3(m-3)-3(m+3)}{(m-3)(m+3)}=0\\\\\dfrac{m^2-6m+9}{(m-3)(m+3)}=0=\dfrac{(m-3)^2}{(m-3)(m+3)}\\\\\dfrac{m-3}{m+3}=0\quad\text{m \ne 3}$

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