During one of the steps when you were subtracting, you made a mistake with a minus sign. You may have incorrectly gotten $\displaystyle{10}{x}-{9}\usepackage{cmbright}\Huge\$ left over after the first subtraction, when it should have been $\displaystyle-{10}{x}-{9}\usepackage{cmbright}\Huge\$ . The correct answer is: $\displaystyle{x}-{10}+\frac{{{41}}}{{{x}+{5}}}\usepackage{cmbright}\Huge\$