What is the solution set to the equation (2)/(7-m)=(4)/(m)-(5-m)/(7-m) A) 4,7 B) 4,5 C) 1,7 D) 4

To solve the equation , we can start by finding a common denominator for the fractions on the right side of the equation. The common denominator is . Multiplying both sides of the equation by , we get: Expanding and simplifying, we have: Multiplying through by to clear the fraction, we get: Rearranging terms, we have: This is a quadratic equation, which can be solved using the quadratic formula or by factoring. Factoring this equation, we get: Setting each factor equal to zero, we have: or Solving for , we get: or However, we must check these solutions in the original equation to ensure they are not extraneous. Plugging into the original equation, we find that it is a valid solution. Plugging into the original equation, we find that it is not a valid solution because it makes the denominator of the first fraction equal to zero.Therefore, the solution set to the equation is , which corresponds to option D.