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help me, please

perform the operations indicated

 

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

ManuelBautista2019  Dec 4, 2017

Best Answer 

 #1
avatar+7096 
+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
 #1
avatar+7096 
+1
Best Answer

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

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