Answer: Last option.
Step-by-step explanation:
Given the equation:
[tex]\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}[/tex]
Follow these steps to solve it:
- Subtract the fractions on the left side of the equation:
[tex]\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}[/tex]
- Using the Difference of squares formula ([tex]a^2-b^2=(a+b)(a-b)[/tex]) we can simplify the denominator of the right side of the equation:
[tex]\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}[/tex]
- Multiply both sides of the equation by [tex](m+3)(3-m)[/tex] and simplify:
[tex]\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}[/tex]
- Multiply both sides by [tex]m-3[/tex]:
[tex](-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)[/tex]
- Apply Distributive property and simplify:
[tex](-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0[/tex]
- Divide both sides of the equation by -6:
[tex]\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0[/tex]
- Factor the equation and solve for "m":
[tex](m-3)^2=0\\\\m=3[/tex]
In order to verify it, you must substitute [tex]m=3[/tex] into the equation and solve it:
[tex]\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}[/tex]
NO SOLUTION
