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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Simplify

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

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

(1 - i)^{13}

\frac{6 ( 7 ^{20} - 5 ^{20} )}{7 ^{20}} - \frac{144}{49}

(5 sin (t) + sin (5 t)) (- 5 sin (t) - 5 sin (5 t))

\frac{a c ( 16 a c - 8 b ^{2} ) + b ^{4}}{4 a ^{2}}

\frac{( x - 3 ) ( x + 3 )}{( x - 4 ) ( x + 4 )}

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