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perform the operations indicated

y2+2y/x+ 2xy +yDivided by y2 - 4 / x+y

Dec 4, 2017

#1
+8961
+1

Is this the right expresion?

$$\frac{y^2+2y}{x^2+2xy+y^2}\div\frac{y^2-4}{x+y}$$

First let's factor the numerators and denominators.

$$=\,\frac{y(y+2)}{x^2+xy +xy+y^2}\div \frac{(y+2)(y-2)}{x+y} \\~\\ =\,\frac{y(y+2)}{x(x+y) +y(x+y)}\div \frac{(y+2)(y-2)}{x+y} \\~\\ =\,\frac{y(y+2)}{(x+y)(x+y)}\div \frac{(y+2)(y-2)}{x+y}$$

Now Invert the second fraction and change to multiplication.

$$=\,\frac{y(y+2)}{(x+y)(x+y)}\cdot \frac{x+y}{(y+2)(y-2)} \\~\\ =\,\frac{y(y+2)(x+y)}{(x+y)(x+y)(y+2)(y-2)}$$

Now reduce the fraction as much as possible.

$$=\,\frac{y}{(x+y)(y-2)}$$

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Dec 4, 2017

#1
+8961
+1

Is this the right expresion?

$$\frac{y^2+2y}{x^2+2xy+y^2}\div\frac{y^2-4}{x+y}$$

First let's factor the numerators and denominators.

$$=\,\frac{y(y+2)}{x^2+xy +xy+y^2}\div \frac{(y+2)(y-2)}{x+y} \\~\\ =\,\frac{y(y+2)}{x(x+y) +y(x+y)}\div \frac{(y+2)(y-2)}{x+y} \\~\\ =\,\frac{y(y+2)}{(x+y)(x+y)}\div \frac{(y+2)(y-2)}{x+y}$$

Now Invert the second fraction and change to multiplication.

$$=\,\frac{y(y+2)}{(x+y)(x+y)}\cdot \frac{x+y}{(y+2)(y-2)} \\~\\ =\,\frac{y(y+2)(x+y)}{(x+y)(x+y)(y+2)(y-2)}$$

Now reduce the fraction as much as possible.

$$=\,\frac{y}{(x+y)(y-2)}$$

hectictar Dec 4, 2017