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

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

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

simplify

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

\frac{x - y - z}{z - x - y}

Solution steps

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

Factor

x^{2} - (y + z)^{2} : (x + y + z) (x - y - z)

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

Factor

z^{2} - (x + y)^{2} : (z + x + y) (z - x - y)

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

Apply the commutative law:

z + x + y = x + y + z

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

Cancel the common factor:

x + y + z

= \frac{x - y - z}{z - x - y}

a^{3} - 0.216

27 y^{3} - 125 z^{3}

ln (n^{2})

x + 3 y - 5 x

(2 a - 1)^{3}

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