# Divide (1/3x^2+7/10*(xy)-1/3y^2)/(x-2/5y)

13×2+710⋅(xy)-13y2x-25y
Simplify the numerator.
Combine 13 and x2.
x23+710⋅(xy)-13y2x-25y
Multiply 710(xy).
Combine x and 710.
x23+x⋅710y-13y2x-25y
Combine x⋅710 and y.
x23+x⋅7y10-13y2x-25y
x23+x⋅7y10-13y2x-25y
Move 7 to the left of x.
x23+7⋅xy10-13y2x-25y
Combine y2 and 13.
x23+7xy10-y23x-25y
To write x23 as a fraction with a common denominator, multiply by 1010.
x23⋅1010+7xy10-y23x-25y
To write 7xy10 as a fraction with a common denominator, multiply by 33.
x23⋅1010+7xy10⋅33-y23x-25y
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply x23 and 1010.
x2⋅103⋅10+7xy10⋅33-y23x-25y
Multiply 3 by 10.
x2⋅1030+7xy10⋅33-y23x-25y
Multiply 7xy10 and 33.
x2⋅1030+7xy⋅310⋅3-y23x-25y
Multiply 10 by 3.
x2⋅1030+7xy⋅330-y23x-25y
x2⋅1030+7xy⋅330-y23x-25y
Combine the numerators over the common denominator.
x2⋅10+7xy⋅330-y23x-25y
To write -y23 as a fraction with a common denominator, multiply by 1010.
x2⋅10+7xy⋅330-y23⋅1010x-25y
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply y23 and 1010.
x2⋅10+7xy⋅330-y2⋅103⋅10x-25y
Multiply 3 by 10.
x2⋅10+7xy⋅330-y2⋅1030x-25y
x2⋅10+7xy⋅330-y2⋅1030x-25y
Combine the numerators over the common denominator.
x2⋅10+7xy⋅3-y2⋅1030x-25y
Rewrite x2⋅10+7xy⋅3-y2⋅1030 in a factored form.
Move 10 to the left of x2.
10⋅x2+7xy⋅3-y2⋅1030x-25y
Multiply 3 by 7.
10×2+21xy-y2⋅1030x-25y
Multiply 10 by -1.
10×2+21xy-10y230x-25y
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=10⋅-10=-100 and whose sum is b=21.
Reorder terms.
10×2-10y2+21xy30x-25y
Reorder -10y2 and 21xy.
10×2+21xy-10y230x-25y
Factor 21 out of 21xy.
10×2+21(xy)-10y230x-25y
Rewrite 21 as -4 plus 25
10×2+(-4+25)(xy)-10y230x-25y
Apply the distributive property.
10×2-4(xy)+25(xy)-10y230x-25y
Move parentheses.
10×2-4xy+25xy-10y230x-25y
10×2-4xy+25xy-10y230x-25y
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(10×2-4xy)+25xy-10y230x-25y
Factor out the greatest common factor (GCF) from each group.
2x(5x-2y)+5y(5x-2y)30x-25y
2x(5x-2y)+5y(5x-2y)30x-25y
Factor the polynomial by factoring out the greatest common factor, 5x-2y.
(5x-2y)(2x+5y)30x-25y
(5x-2y)(2x+5y)30x-25y
(5x-2y)(2x+5y)30x-25y
(5x-2y)(2x+5y)30x-25y
Simplify the denominator.
Combine y and 25.
(5x-2y)(2x+5y)30x-y⋅25
Move 2 to the left of y.
(5x-2y)(2x+5y)30x-2⋅y5
To write x as a fraction with a common denominator, multiply by 55.
(5x-2y)(2x+5y)30x⋅55-2y5
Combine x and 55.
(5x-2y)(2x+5y)30x⋅55-2y5
Combine the numerators over the common denominator.
(5x-2y)(2x+5y)30x⋅5-2y5
Move 5 to the left of x.
(5x-2y)(2x+5y)305x-2y5
(5x-2y)(2x+5y)305x-2y5
Multiply the numerator by the reciprocal of the denominator.
(5x-2y)(2x+5y)30⋅55x-2y
Cancel the common factor of 5x-2y.
Cancel the common factor.
(5x-2y)(2x+5y)30⋅55x-2y
Rewrite the expression.
2x+5y30⋅5
2x+5y30⋅5
Cancel the common factor of 5.
Factor 5 out of 30.
2x+5y5(6)⋅5
Cancel the common factor.
2x+5y5⋅6⋅5
Rewrite the expression.
2x+5y6
2x+5y6
Split the fraction 2x+5y6 into two fractions.
2×6+5y6
Cancel the common factor of 2 and 6.
Factor 2 out of 2x.
2(x)6+5y6
Cancel the common factors.
Factor 2 out of 6.
2×2⋅3+5y6
Cancel the common factor.
2×2⋅3+5y6
Rewrite the expression.
x3+5y6
x3+5y6
x3+5y6
Divide (1/3x^2+7/10*(xy)-1/3y^2)/(x-2/5y)