Question

50 points, question down below. :)

Answer 1

3

Explanation:

The given equation is ,

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

Firstly lets try to simplify the LHS .Wr have ,

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

Simplify using identity , we get ,

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

On futher simplyfing we will get a equation as ,

`\implies m^2-6m +9= m^2 -9 \\\\\implies 6m = 18 \\\\\implies \underline{\underline{ x = 3 }}`

Hence the required answer is 3 .

Answer 2

`The\ domain:\\m+3\\eq0\ \wedge\ 3-m\\eq0\\m\\eq-3\ \wedge\ m\\eq3\\\\(3)/(m+3)-(m)/(3-m)=(m^2+9)/(m^2-9)\\\\(3)/(m+3)-(m)/(-(m-3))=(m^2+9)/(m^2-9)\\\\(3)/(m+3)+(m)/(m-3)=(m^2+9)/(m^2-9)\\\\(3(m-3))/((m+3)(m-3))+(m(m+3))/((m+3)(m-3))=(m^2+9)/(m^2-9)\\\\(3m-9+m^2+3m)/(m^2-9)=(m^2+9)/(m^2-9)\iff m^2+6m-9=m^2+9\ \ \ \ |-m^2\\\\6m-9=9\ \ \ \ |+9\\\\6m=18\ \ \ \ |:6\\\\\boxed{m=3\\otin D}`

Answer: No solution