Asked by Swakena Jackson on May 17, 2024
Verified
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
A) 6(x+y) x−y,x≠y\frac { 6 ( x + y ) } { x - y } , x \neq yx−y6(x+y) ,x=y
B) 6(y−x) xy,x≠−y\frac { 6 ( y - x ) } { x y } , x \neq - yxy6(y−x) ,x=−y
C) 6(x−y) x+y,x≠−y\frac { 6 ( x - y ) } { x + y } , x \neq - yx+y6(x−y) ,x=−y
D) 6(x−y) xy,x≠y\frac { 6 ( x - y ) } { x y } , x \neq yxy6(x−y) ,x=y
E) 6(x+y) xy(x−y) ,x≠−y\frac { 6 ( x + y ) } { x y ( x - y ) } , x \neq - yxy(x−y) 6(x+y) ,x=−y
Combine
To join two or more items together to form a single entity or to merge separate elements into a cohesive whole.
Simplify
The process of writing an expression in a more compact or simplified form without changing its value, by performing all possible operations and reducing complexity.
- Apply the processes of addition and subtraction to fractions with variables.
Verified Answer
JD
Jennifer DeleonMay 18, 2024
Final Answer :
B
Explanation :
To combine and simplify the given expression, factor out common terms and find a common denominator. The given expression is 6yx2+xy−6xxy+y2\frac { 6 y } { x ^ { 2 } + x y } - \frac { 6 x } { x y + y ^ { 2 } }x2+xy6y−xy+y26x . Notice that both denominators can be written as a product of xxx and yyy in some form, making the common denominator xyxyxy . Simplifying within this framework leads to the expression 6(y−x)xy\frac { 6 ( y - x ) } { x y }xy6(y−x) , which matches choice B.
Learning Objectives
- Apply the processes of addition and subtraction to fractions with variables.