What is (\frac{2xy^3z)/(x^2-xz)}{(4y^2z)/(x-z)} ?

The solution to (\frac{2xy^3z)/(x^2-xz)}{(4y^2z)/(x-z)} is y/2

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simplify (\frac{2xy^3z)/(x^2-xz)}{(4y^2z)/(x-z)}

simplify

\frac{\frac{2 x y ^{3} z}{x ^{2} - x z}}{\frac{4 y ^{2} z}{x - z}}

\frac{y}{2}

Solution steps

\frac{\frac{2 x y ^{3} z}{x ^{2} - x z}}{\frac{4 y ^{2} z}{x - z}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{2 x y ^{3} z ( x - z )}{( x ^{2} - x z ) \cdot 4 y ^{2} z}

Cancel the common factor:

z

= \frac{2 x y ^{3} ( x - z )}{( x ^{2} - x z ) \cdot 4 y ^{2}}

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

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

Apply exponent rule:

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

y^{3} = y^{2} y

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

Cancel the common factor:

y^{2}

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

Factor

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

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

Cancel the common factor:

x

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

Cancel the common factor:

x - z

= \frac{y}{2}

2 x^{2} + 12 x - 14 = 0

p (c - d) + c - d

\frac{5 !}{2 !}

\frac{0}{- 11}

(1 + 2)^{2}

What is (\frac{2xy^3z)/(x^2-xz)}{(4y^2z)/(x-z)} ?
The solution to (\frac{2xy^3z)/(x^2-xz)}{(4y^2z)/(x-z)} is y/2