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

The solution to (y-x(x/y))/(y^2) is (y^2-x^2)/(y^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

Apply rule:

(a) = a

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

y y^{2} : y^{3}

= \frac{y ^{2} - x ^{2}}{y ^{3}}

x^{3} + 16 x^{2} + 28 x

25 x^{2} - 10 x y + y^{2}

x (2 x + 9) \geq 0

9 - 2 x^{2} = 0