# Divide ((x^2-4)/(21x))/((2-4)/(7xy))

x2-421×2-47xy
Multiply the numerator by the reciprocal of the denominator.
x2-421x⋅7xy2-4
Cancel the common factor of 7x.
Factor 7x out of 21x.
x2-47x(3)⋅7xy2-4
Factor 7x out of 7xy.
x2-47x(3)⋅7x(y)2-4
Cancel the common factor.
x2-47x⋅3⋅7xy2-4
Rewrite the expression.
x2-43⋅y2-4
x2-43⋅y2-4
Multiply x2-43 and y2-4.
(x2-4)y3(2-4)
Simplify the numerator.
Rewrite 4 as 22.
(x2-22)y3(2-4)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=2.
(x+2)(x-2)y3(2-4)
(x+2)(x-2)y3(2-4)
Subtract 4 from 2.
(x+2)(x-2)y3⋅-2
Multiply 3 by -2.
(x+2)(x-2)y-6
Move the negative in front of the fraction.
-(x+2)(x-2)y6
Reorder factors in -(x+2)(x-2)y6.
-y(x+2)(x-2)6
Apply the distributive property.
-(yx+y⋅2)(x-2)6
Move 2 to the left of y.
-(yx+2⋅y)(x-2)6
Expand (yx+2y)(x-2) using the FOIL Method.
Apply the distributive property.
-yx(x-2)+2y(x-2)6
Apply the distributive property.
-yx⋅x+yx⋅-2+2y(x-2)6
Apply the distributive property.
-yx⋅x+yx⋅-2+2yx+2y⋅-26
-yx⋅x+yx⋅-2+2yx+2y⋅-26
Combine the opposite terms in yx⋅x+yx⋅-2+2yx+2y⋅-2.
Reorder the factors in the terms yx⋅-2 and 2yx.
-yx⋅x-2xy+2xy+2y⋅-26
-yx⋅x+0+2y⋅-26
-yx⋅x+2y⋅-26
-yx⋅x+2y⋅-26
Simplify each term.
Multiply x by x by adding the exponents.
Move x.
-y(x⋅x)+2y⋅-26
Multiply x by x.
-yx2+2y⋅-26
-yx2+2y⋅-26
Multiply -2 by 2.
-yx2-4y6
-yx2-4y6
Split the fraction yx2-4y6 into two fractions.
-(yx26+-4y6)
Cancel the common factor of -4 and 6.
Factor 2 out of -4y.
-(yx26+2(-2y)6)
Cancel the common factors.
Factor 2 out of 6.
-(yx26+2(-2y)2(3))
Cancel the common factor.
-(yx26+2(-2y)2⋅3)
Rewrite the expression.
-(yx26+-2y3)
-(yx26+-2y3)
-(yx26+-2y3)
Move the negative in front of the fraction.
-(yx26-2y3)
Divide ((x^2-4)/(21x))/((2-4)/(7xy))