Correct the error. \( \frac{x}{x+2}+\frac{4}{x-5}=\square \)

To add   x/(x + 2) + 4/(x – 5) you must use a common denominator. The common denominator is (x + 2)(x – 5). Multiply numerator and denominator of each fraction by the factor missing from its denominator:   • For x/(x + 2), multiply by (x – 5)/(x – 5).   • For 4/(x – 5), multiply by (x + 2)/(x + 2). This gives   [x(x – 5)]/[(x + 2)(x – 5)] + [4(x + 2)]/[(x + 2)(x – 5)]. Now combine the fractions:   = [x(x – 5) + 4(x + 2)]/[(x + 2)(x – 5)]. Next, expand the numerators:   x(x – 5) = x² – 5x   4(x + 2) = 4x + 8 So the numerator becomes:   x² – 5x + 4x + 8 = x² – x + 8. Thus, the correct expression is   (x² – x + 8)/[(x + 2)(x – 5)]. So, the error is corrected by writing   x/(x + 2) + 4/(x – 5) = (x² – x + 8)/[(x + 2)(x – 5)].