What is ((y-x))/((x^2-y^2)) ?

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

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simplify ((y-x))/((x^2-y^2))

simplify

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

- \frac{1}{x + y}

Solution steps

\frac{y - x}{x ^{2} - y ^{2}}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

x^{2} - y^{2} = (x + y) (x - y)

= \frac{y - x}{( x + y ) ( x - y )}

(x + y) (x - y) = - (x + y) (y - x)

= \frac{y - x}{- ( x + y ) ( y - x )}

Cancel the common factor:

y - x

= \frac{1}{- ( x + y )}

Apply the fraction rule:

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

= - \frac{1}{x + y}

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x^{3} + 2197