What is (40x^4y+16x^2y^3)/(60x^2y^2-36xy^3) ?

The solution to (40x^4y+16x^2y^3)/(60x^2y^2-36xy^3) is (2x(5x^2+2y^2))/(3y(5x-3y))

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simplify (40x^4y+16x^2y^3)/(60x^2y^2-36xy^3)

simplify

\frac{40 x ^{4} y + 16 x ^{2} y ^{3}}{60 x ^{2} y ^{2} - 36 x y ^{3}}

\frac{2 x ( 5 x ^{2} + 2 y ^{2} )}{3 y ( 5 x - 3 y )}

Solution steps

\frac{40 x ^{4} y + 16 x ^{2} y ^{3}}{60 x ^{2} y ^{2} - 36 x y ^{3}}

Factor

40 x^{4} y + 16 x^{2} y^{3} : 8 x^{2} y (5 x^{2} + 2 y^{2})

= \frac{8 x ^{2} y ( 5 x ^{2} + 2 y ^{2} )}{60 x ^{2} y ^{2} - 36 x y ^{3}}

Factor

60 x^{2} y^{2} - 36 x y^{3} : 12 x y^{2} (5 x - 3 y)

= \frac{8 x ^{2} y ( 5 x ^{2} + 2 y ^{2} )}{12 x y ^{2} ( 5 x - 3 y )}

Factor the number:

8 = 4 \cdot 2

= \frac{4 \cdot 2 x ^{2} y ( 5 x ^{2} + 2 y ^{2} )}{12 x y ^{2} ( 5 x - 3 y )}

Factor the number:

12 = 4 \cdot 3

= \frac{4 \cdot 2 x ^{2} y ( 5 x ^{2} + 2 y ^{2} )}{4 \cdot 3 x y ^{2} ( 5 x - 3 y )}

Cancel the common factor:

4

= \frac{2 x ^{2} y ( 5 x ^{2} + 2 y ^{2} )}{3 x y ^{2} ( 5 x - 3 y )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{2} = xx

= \frac{2 xx y ( 5 x ^{2} + 2 y ^{2} )}{3 x y ^{2} ( 5 x - 3 y )}

Cancel the common factor:

x

= \frac{2 x y ( 5 x ^{2} + 2 y ^{2} )}{3 y ^{2} ( 5 x - 3 y )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{2} = yy

= \frac{2 x y ( 5 x ^{2} + 2 y ^{2} )}{3 yy ( 5 x - 3 y )}

Cancel the common factor:

y

= \frac{2 x ( 5 x ^{2} + 2 y ^{2} )}{3 y ( 5 x - 3 y )}

x - 1 \leq 4 x + 5

5 n + 3 = 14 - 6 n

\frac{2 ^{4}}{2 ^{6}}

x^{2} - 3 x = 7

(\frac{r}{r ^{4}})^{3}

What is (40x^4y+16x^2y^3)/(60x^2y^2-36xy^3) ?
The solution to (40x^4y+16x^2y^3)/(60x^2y^2-36xy^3) is (2x(5x^2+2y^2))/(3y(5x-3y))