How is this one solved?

Answer:   see belowStep-by-step explanation:This is solved by simplifying each expression and identifying the column heading it matches.1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5)) = (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply = (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel = 3x/(x -2) . . . . matches column 1__2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5)) = (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor = (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor = ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator = (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product = (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms = (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator = x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2__3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x) = 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1__4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x) = 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2__5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)__6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.