What is ((x-y)^3)/((y-x)^5) ?

The solution to ((x-y)^3)/((y-x)^5) is -1/((x-y)^2)

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simplify ((x-y)^3)/((y-x)^5)

simplify

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

- \frac{1}{( x - y ) ^{2}}

Solution steps

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

(y - x)^{5} = - (x - y)^{5}

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

Apply exponent rule:

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

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

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

Cancel the common factor:

(x - y)^{3}

= \frac{1}{- ( x - y ) ^{2}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{( x - y ) ^{2}}

(3 x + 3 y)^{3}

x \cdot y^{5} - x^{5} \cdot y

3 x \cdot y^{2} - 9 x^{2} \cdot y

39 x y \cdot z^{2} - 13 x^{2} \cdot y^{2} \cdot z^{2} + 65 x^{3} \cdot y^{3} \cdot z

\frac{( ( a - b ) ^{2} + ( b - c ) ^{2} + ( a - c ) ^{2} )}{12}

What is ((x-y)^3)/((y-x)^5) ?
The solution to ((x-y)^3)/((y-x)^5) is -1/((x-y)^2)