20/(16+m) + 12/m = 1First, we'll simplify the equation by finding a common denominator:(20m + 12(16+m)) / (m(16+m)) = 1Now, distribute and combine like terms in the numerator:(20m + 192 + 12m) / (m(16+m)) = 1Combine the m terms in the numerator:(32m + 192) / (m(16+m)) = 1Multiply both sides by m(16+m) to clear the fraction:32m + 192 = m(16+m)Expand the right side:32m + 192 = 16m + m^2Rearrange the equation to bring all terms to one side and set equal to zero:m^2 - 20m - 192 = 0Now we can factor the quadratic equation:(m - 24)(m + 8) = 0This gives us two possible values for m:m - 24 = 0 or m + 8 = 0Solving each equation separately:m = 24 or m = -8These are the two solutions to the equation. However, we must check if they satisfy the original equation. Plugging in m = 24:20/(16+24) + 12/24 = 120/40 + 1/2 = 11/2 + 1/2 = 11 = 1The value of m = 24 satisfies the original equation. For m = -8:20/(16-8) + 12/-8 = 120/8 - 1.5 = 12.5 - 1.5 = 11 = 1The value of m = -8 also satisfies the original equation. Therefore, both m = 24 and m = -8 are valid solutions.