Simplify the expression. $\frac { 6 x ^ { 2 } - x y - y ^ { 2 } } { 3 x ^ { 2 } - 5 y x - 2 y ^ { 2 } } \cdot \frac { x ^ { 2 } - 3 x y + 2 y ^ { 2 } } { x ^ { 2 } + x y - 2 y ^ { 2 } }$
A) $\frac { 2 x + y } { x - 2 y }$
B) $\frac { x + 2 y } { 2 x - y }$
C) $\frac { 2 x - y } { x + 2 y }$
D) $\frac { 2 - x y } { 2 x + y }$
E) $\frac { x + y + 2 } { x - 2 y - 2 }$

Question

Quizplus · Accepted Answer

First, let's simplify the numerator by factoring:

\begin{align*}
6 x^2 - x y - y^2 &= (2x - y)(3x + y)\
x^2 - 3xy + 2y^2 &= (x - y)(x - 2y)
\end{align*}

Next, let's simplify the denominator by factoring:

\begin{align*}
3 x^2 - 5 y x - 2 y^{2} &= (3x + y)(x - 2y)\
x^2 + x y - 2 y^2 &= (x - y)(x + 2y)
\end{align*}

Now we can simplify the expression:

\begin{align*}
\frac{6 x^{2} - x y - y^{2}}{3 x^{2} - 5 y x - 2 y^{2}} \cdot \frac{x^2 - 3xy + 2y^2}{x^2 + xy - 2y^2} &= \frac{(2x - y)(3x + y)}{(3x + y)(x - 2y)} \cdot \frac{(x - y)(x - 2y)}{(x - y)(x + 2y)}\
&= \frac{(2x - y)}{(x + 2y)}
\end{align*}

Therefore, the answer is choice C.

Simplify the Expression A) 2x+yx−2y\frac { 2 x + y } { x - 2 y }x−2y2x+y​

Simplify the Expression A) $\frac { 2 x + y } { x - 2 y }$