simplify help

jvignacio · #1 $Old$ 11-19-2008, 11:17 PM

$(x+\frac{y^2}{x-y})/(\frac{x^3+y^3}{x^2-y^2})$

$(\frac {x}{x}+\frac{y^2}{x-y})/(\frac{x^3+y^3}{x^2-y^2})$

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

is this correcT? thank u

Soroban · #2 $Old$ 11-19-2008, 11:33 PM

Hello, jvignacio!

Quote:

Simplify: . $\left(x+\frac{y^2}{x-y}\right) \div \left(\frac{x^3+y^3}{x^2-y^2}\right)$

The first expression is: . $\frac{x}{1}\cdot\frac{x-y}{x-y} \;+\;\frac{y^2}{x-y}\;=\;\frac{x(x-y) + y^2}{x-y} \;=\;\frac{x^2-xy+y^2}{x-y}$

The second expression is: . $\frac{(x+y)(x^2-xy+y^2)}{(x-y)(x+y)} \;=\;\frac{x^2-xy+r^2}{x-y}$

The problem becomes: . $\frac{x^2-xy+y^2}{x-y} \div \frac{x^2-xy+y^2}{x-y} \;=\;\frac{x^2-xy+y^2}{x-y}\cdot\frac{x-y}{x^2-xy+y^2} \;=\;\boxed{1}$