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

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

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

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

x^{2} - y^{2} x^{2} - y^{2} = x^{2} - y^{2}

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

Cancel the common factor:

x - y

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

4 x^{2} y^{4} - 36 z^{2} t^{2}

lo g_{4} (\frac{( x ^{3} \cdot ( x + 3 ) )}{( 3 x - 2 )})

(x + 3) (x^{2} - 6 x + 9)

\frac{( x ^{4} - 16 )}{( x ^{3} - 8 )}

(16 z)^{- 3} \cdot (4 z)^{3}

What is (((x-y)*sqrt(x-y)))/((sqrt(x^2-y^2))) ?
The solution to (((x-y)*sqrt(x-y)))/((sqrt(x^2-y^2))) is (sqrt(x-y)sqrt(x^2-y^2))/(x+y)