\( \frac { 5 x } { 2 x - 5 } = \frac { \square } { x ( 2 x - 5 ) ( x + 4 ) } \)

To solve for the missing value in the equation \( \frac { 5 x } { 2 x - 5 } = \frac { \square } { x ( 2 x - 5 ) ( x + 4 ) } \), we can cross-multiply. This would give us \( 5x \cdot x(2x - 5)(x + 4) = \square \cdot (2x - 5) \). Now, we simplify the left side. The denominator \( (2x - 5) \) cancels out from both sides, yielding \( 5x (x + 4) = \square \). Now calculate \( 5x(x + 4) = 5x^2 + 20x \). So we have found that the missing value in the equation is \( 5x^2 + 20x \). So, the completed equation becomes: \[ \frac { 5 x } { 2 x - 5 } = \frac { 5 x^2 + 20 x } { x ( 2 x - 5 ) ( x + 4 ) } \]. Keep in mind that when substituting values, you should not let \( x \) equal values that would make the denominator zero, like \( \frac{5}{2} \).