Question

Completely simplify the rational expression LaTeX: \frac{7x}{3y} + \frac{12x}{9y}

Answer 1

Answer:

$\frac{11x}{3y}$

Step-by-step explanation:

$\frac{7x}{3y} + \frac{12x}{9y}$

To add the two fractions, you need a common denominator.  In this case, the lowest common denominator (LCD) is 9y.  That's because 9y is divisible by both 3y and 9y.

The first fraction must be changed so that its denominator is 9y.  Do this by multiplying both numerator and denominator by 3.

$\frac{7x}{3y}\cdot\frac{3}{3}+\frac{21x}{9y}=\frac{21x}{9y}+\frac{12x}{9y}\\=\frac{21x+12x}{9y}\\=\frac{33x}{9y}$

Finally, this answer can be simplified ("reduced") by dividing both numerator and denominator by 3, their greatest common factor.