x2-421×2-47xy

Multiply the numerator by the reciprocal of the denominator.

x2-421x⋅7xy2-4

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)

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

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

Reorder the factors in the terms yx⋅-2 and 2yx.

-yx⋅x-2xy+2xy+2y⋅-26

Add -2xy and 2xy.

-yx⋅x+0+2y⋅-26

Add yx⋅x and 0.

-yx⋅x+2y⋅-26

-yx⋅x+2y⋅-26

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)

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))