Help with question please (1 Viewer)

dabatman · Feb 27, 2017

Hi the question is attached,

Can someone please help, I know its simple but I keep messing it up all the time.

This question is from Maths in focus Extension 1 preliminary

1729 · Feb 27, 2017

dabatman said:
Hi the question is attached,

Can someone please help, I know its simple but I keep messing it up all the time.

This question is from Maths in focus Extension 1 preliminary

$$\noindent A nice way of simplifying through some denominator manipulation, \\ \begin{align*} \frac{x+y}{x-y} + \frac{x}{y-x} - \frac{y}{y^2-x^2} &= \frac{x+y}{x-y} - \frac{x}{x-y} + \frac{y}{(x+y)(x-y)} \\ &= \frac{y(x+y)+y}{x^2-y^2} \\ &= \frac{y(x+y+1)}{x^2 - y^2} \textrm{ or } \frac{y^2+xy+y}{x^2-y^2} \end{align*}$

boredofstudiesuser1 · Feb 27, 2017

1729 said:
$$\noindent A nice way of simplifying through some denominator manipulation; \\ \begin{align*} \frac{x+y}{x-y} + \frac{x}{y-x} - \frac{y}{y^2-x^2} &= \frac{x+y}{x-y} - \frac{x}{x-y} + \frac{y}{(x+y)(x-y)} \\ &= \frac{x^2 + 2xy + y^2 -x(x + y)+ y}{x^2-y^2} \\ &= \frac{y^2+xy+y}{x^2 - y^2} \end{align*}$

Wouldn't it be 3xy?

He-Mann · Feb 27, 2017

1729 said:
$$\noindent A nice way of simplifying through some denominator manipulation; \\ \begin{align*} \frac{x+y}{x-y} + \frac{x}{y-x} - \frac{y}{y^2-x^2} &= \frac{x+y}{x-y} - \frac{x}{x-y} + \frac{y}{(x+y)(x-y)} \\ &= \frac{x^2 + 2xy + y^2 -x(x + y)+ y}{x^2-y^2} \\ &= \frac{y(x+y+1)}{x^2 - y^2} \textrm{ or } \frac{y^2+xy+y}{x^2-y^2} \end{align*}$

$$\noindent Optimise your process with this, $\\ \frac{x+y}{x-y} - \frac{x}{x-y} + \frac{y}{x^2-y^2} =\frac{y}{x-y} + \frac{y}{(x-y)(x+y)}$

1729 · Feb 27, 2017

boredofstudiesuser1 said:
Wouldn't it be 3xy?

When we isolate the terms we have 2xy - xy = xy.

boredofstudiesuser1 · Feb 27, 2017

1729 said:
When we isolate the terms we have 2xy - xy = xy.

Ohh I thought it was (x-y). My bad

dabatman · Feb 28, 2017

thanks so much guys

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