Combine and simplify. $\frac { 6 y } { x ^ { 2 } + x y } - \frac { 6 x } { x y + y ^ { 2 } }$
A) $\frac { 6 ( x + y ) } { x - y } , x \neq y$
B) $\frac { 6 ( y - x ) } { x y } , x \neq - y$
C) $\frac { 6 ( x - y ) } { x + y } , x \neq - y$
D) $\frac { 6 ( x - y ) } { x y } , x \neq y$
E) $\frac { 6 ( x + y ) } { x y ( x - y ) } , x \neq - y$

Question

Quizplus · Accepted Answer

To combine and simplify the given expression, factor out common terms and find a common denominator. The given expression is $\frac { 6 y } { x ^ { 2 } + x y } - \frac { 6 x } { x y + y ^ { 2 } }$. Notice that both denominators can be written as a product of $x$ and $y$ in some form, making the common denominator $xy$. Simplifying within this framework leads to the expression $\frac { 6 ( y - x ) } { x y }$, which matches choice B.

Combine and Simplify 6yx2+xy−6xxy+y2\frac { 6 y } { x ^ { 2 } + x y } - \frac { 6 x } { x y + y ^ { 2 } }x2+xy6y​−xy+y26x​

Combine and Simplify $\frac { 6 y } { x ^ { 2 } + x y } - \frac { 6 x } { x y + y ^ { 2 } }$