Rational complex expression help.

[usctrojanfan]

Im suppose to simplify
x^-1-y^-1
__________
x^2-y^2
________ here is what i've done, x/1-1/y /(x+y(x-y)/xy i used the axd and bxc method so I got: xy/x(x+y)y(x-y)= xy/x^2+xy-xy+y^2= xy/(x+y)(x+y) The answer on the calculator says its
xy



what am I doing wrong? [FONT=MathJax_Main]−[FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][/FONT]

 

[usctrojanfan]

hello i re did the problem, i got y-x/(x+y)(x-y) and i did (-1) to the numerator so i got (x-y)/(x+y)(x-y) and i cancelled out the (x-y) so my final answer is -1/x+y i'm pretty sure that is the right answer can anyone double check for me?

 

[Deleted member 4993]

Im suppose to simplify
x^-1-y^-1
__________
x^2-y^2
________ here is what i've done, x/1-1/y /(x+y(x-y)/xy i used the axd and bxc method so I got: xy/x(x+y)y(x-y)= xy/x^2+xy-xy+y^2= xy/(x+y)(x+y) The answer on the calculator says its
xy



what am I doing wrong? [FONT=MathJax_Main]−[FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][/FONT]

\(\displaystyle \displaystyle{\frac{\frac{1}{x} - \frac{1}{y}}{x^2 - y^2}}\)

\(\displaystyle =\ \displaystyle{\frac{\frac{y - x}{xy}}{(x+y)(x-y)}}\)

\(\displaystyle =\ \displaystyle{- \frac{1}{xy(x+y)}}\)

This is what you should get......

 

[usctrojanfan]

ok i got that answer, except do we have to put the xy in the xy(x+y) because my professor doesn't put that I don't think.

 

[Deleted member 4993]

ok i got that answer, except do we have to put the xy in the xy(x+y) because my professor doesn't put that I don't think.

Can you simplify a similar expression with numbers? For example:

\(\displaystyle \displaystyle{\frac{\frac{1}{5} - \frac{1}{7}}{5^2 - 7^2}}\)

Compare the result with the result of:

\(\displaystyle =\ \displaystyle{- \frac{1}{5*7(5+7)}}\)

 

[Deleted member 4993]

hello i re did the problem, i got y-x/(x+y)(x-y) and i did (-1) to the numerator so i got (x-y)/(x+y)(x-y) and i cancelled out the (x-y) so my final answer is -1/x+y i'm pretty sure that is the right answer can anyone double check for me?

That is incorrect.

Replace x with 5 and y with 7 and compare values of your answer and the original expression.

 

[usctrojanfan]

Hello Thank you for your help in this answer [FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main])[/FONT] we usaully don't include the (xy) because it's the lcd and was timed out, or atleast that's how my proffesor likes the answer, so it would be -1 over (x-y) if that makes sense to you? because xy was timed by everything so technically I see what you mean. But it's basically same answer correct? I assume it's preference of the professor?

 

[Deleted member 4993]

Hello Thank you for your help in this answer [FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main][/FONT][FONT=MathJax_Main][/FONT][FONT=MathJax_Math-italic]/[[/FONT][FONT=MathJax_Math-italic][/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT] we usaully don't include the (xy) because it's the lcd and was timed out, or atleast that's how my proffesor likes the answer, so it would be -1 over (x-y) if that makes sense to you? because xy was timed by everything so technically I see what you mean. But it's basically same answer correct? I assume it's preference of the professor?

No .... those are not same - use numbers as I had suggested and you'll see the difference.