- #1
Taylor_1989
- 400
- 14
I would just like someone to check my math on this, because I am not sure that I am doing it the right way. I will show step by step.
Put over common denominator: [itex]\frac{1}{x} + \frac{x}{x+y} + \frac{y}{x-y}[/itex]
1. common denominator: [itex]\frac{x^2-y^2}{x(x^2-y^2)} + \frac{x*x(x-y)}{x(x^2-y^2)}+\frac{y*x(x+y)}{x(x^2-y^2)}[/itex]
2. adding fractions: [itex]x^2-y^2 + x^2(x-y)+xy(x+y) \rightarrow x^2-y^2 + x^3-x^2y+x^2y+xy^2 \rightarrow x^3+x^2-y^2+xy^2[/itex]
The part I am confused with is that, I have to do the multiplication before I expand the brackets, now I thought you always expand the brackets first. This is why I think I have done the wrong method to get the right answer. Can someone set me right, if i have gone wrong somewhere. Big thanks in advanced.
Put over common denominator: [itex]\frac{1}{x} + \frac{x}{x+y} + \frac{y}{x-y}[/itex]
1. common denominator: [itex]\frac{x^2-y^2}{x(x^2-y^2)} + \frac{x*x(x-y)}{x(x^2-y^2)}+\frac{y*x(x+y)}{x(x^2-y^2)}[/itex]
2. adding fractions: [itex]x^2-y^2 + x^2(x-y)+xy(x+y) \rightarrow x^2-y^2 + x^3-x^2y+x^2y+xy^2 \rightarrow x^3+x^2-y^2+xy^2[/itex]
The part I am confused with is that, I have to do the multiplication before I expand the brackets, now I thought you always expand the brackets first. This is why I think I have done the wrong method to get the right answer. Can someone set me right, if i have gone wrong somewhere. Big thanks in advanced.