Answer: (A) [tex]\frac{x^{2}+14x}{9x^{2}}[/tex]
Step-by-step explanation:
[tex]\frac{2x}{x^{2}}[/tex] + [tex]\frac{x-4}{9x}[/tex]
= [tex]\frac{2x}{x^{2}}*(\frac{9}{9})[/tex] + [tex]\frac{x-4}{9x}*(\frac{x}{x})[/tex]
= [tex]\frac{18x}{9x^{2}}[/tex] + [tex]\frac{x^{2}-4x}{9x^{2}}[/tex]
= [tex]\frac{18x+x^{2}-4x}{9x^{2}}[/tex]
= [tex]\frac{x^{2}+14x}{9x^{2}}[/tex]
NOTE: This was an odd question because you should reduce the first fraction [tex]\frac{2x}{x^{2}}[/tex] to [tex]\frac{2}{x}[/tex] before finding the common denominator. The simplified answer is: [tex]\frac{x+14}{9x}[/tex]
