Simplify.
-$$\frac { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } } { 9 y - 18 x }$$

Question

Quizplus · Accepted Answer

To simplify the expression, we first factor the numerator: 
$$\frac{  \frac{1}{x^2} - \frac{4}{y^2}}{9y-18x} = \frac{\frac{1}{x^2}\left(1-\frac{4x^2}{y^2}\right)}{9(y-2x)} = \frac{1}{x^2y^2}\left(\frac{y^2-4x^2}{9(y-2x)}\right)$$
Then we can factor the numerator further using the difference of squares: 
$$\frac{1}{x^2y^2}\left(\frac{(y+2x)(y-2x)}{9(y-2x)}\right) = \frac{1}{x^2y^2}\left(\frac{y+2x}{9}\right)$$
Finally, we can cancel the $(y-2x)$ factor in the denominator with the same factor in the numerator, leaving us with: 
$$\frac{1}{x^2y^2}\left(\frac{y+2x}{9}\right) = \frac{y+2x}{9x^2y^2}$$ 
Therefore, the answer is D.

Simplify - 1x2−4y29y−18x\frac { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } } { 9 y - 18 x }9y−18xx21​−y24​​

Simplify
- $\frac { \frac { 1 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } } { 9 y - 18 x }$