How would you simplify this equation??
((1/x)-(1/y))/(y^2-x^2)
This doesn't look like an equation. There is no equal sign.
you must mean "simplify"
((1/x)-(1/y))/(y^2-x^2)
= ( (y-x)/(xy) ) / ((y-x)(y+x) )
= (y-x)/( (xy)(y+x)(y-x) )
= 1/(xy(y+x) ) , y≠x
Oops, I left the equal sign out!
The problem would actually be:
((1/x)-(1/y))/(y^2-x^2)= ____
Thank you, Reiny!!
To simplify this equation, let's break it down into smaller steps:
Step 1: Simplify the expression inside the parentheses:
(1/x) - (1/y) = (y - x) / (xy)
Step 2: Simplify the expression in the denominator:
y^2 - x^2 = (y + x)(y - x)
Step 3: Substitute the simplified expressions from Step 1 and Step 2 back into the original equation:
((y - x) / (xy)) / ((y + x)(y - x))
Step 4: Cancel out the common factors:
The (y - x) terms in the numerator and denominator simplify to 1, so they can be canceled out:
1 / (xy(y + x))
Therefore, the simplified form of the equation is 1 / (xy(y + x)).