Question

please help me simplify this

x/y-y/x
_________
1/x^2-1/y^2

Answer 1

\[\frac{ \frac{ x }{ y }-\frac{ y }{ x } }{ \frac{ 1 }{ x^2 } -\frac{ 1 }{ y^2 }}\]First separate the equations so it can look more simpler.\[(\frac{ x }{ y }-\frac{ y }{ x })\div (\frac{ 1 }{ x^2 }-\frac{ 1 }{ y^2 })\]

Answer 2

When you flip the second equation, the division sign will change to a multiplication sign.\[(\frac{ x }{ y }-\frac{ y }{ x })\times(x^2-y^2)\]

Answer 3

yes and then what happens to the denominator?

Answer 4

Look at the first equation now and try to get the denominator's the same by cross multiplying.\[(\frac{ x(x) }{ y(x) }-\frac{ y(y) }{ x(y) })\]

Answer 5

\[(\frac{ x^2 }{ xy }-\frac{ y^2 }{ xy })=(\frac{ x^2-y^2 }{ xy })\]

Answer 6

Now the equation looks like this:\[(\frac{ x^2-y^2 }{ xy })\times(x^2-y^2)\]

Answer 7

The original denominator is made up of 2 different fractions. So they don't have a single reciprocal.

Solve these problems by multiplying by 1in the form of the least common denominator divided by itself. The least common denominator of x, y, x², and y² is x²y².