Simplify (x+y^-1)^-1.?

Question

i keep gettin y/x but dont think its correct. is it?

Answer 1

You have to multiply the exponents from the with the exponent on the outside of the ( )'s

[x^(1 x -1)] + [y^(-1 x -1)]

x^-1 + y^1

x^-1 + y

Answer 2

It's the same as

(x + 1/y)^-1

1/(x + 1/y)

The part inside the parentheses:

x + 1/y = (xy + 1)/y

so

1/((xy + 1)/y)

= y / (xy + 1)

and that does not simplify any further, I don't think.

Answer 3

It's not.  That would be the correct simplification for (x*y^-1)^-1.

I don't see any simplification beyond 1/(x+(1/y))

Answer 4

Remember x^-a =1/x  or y^-1 = 1/y

Any expression to the -1 power is the expression over 1.

remember also: Any fraction expression under 1 is the reciprocal. For example:

1/(1/x)=x

1/(x/a)= a/x

Remember to find the fraction expression common denominator before flipping.

1/(x+(1/y)) need to find common denominator of x+(1/y) then to move to the numerator or top, take the reciprocal of denominator.

Common denominator is y and the fraction becomes

xy/y + 1/y = (xy+1)/y

Now we have 1/[(xy+1)/y]

which is an expression for the reciprocal of (xy+1)/y = y/(xy+1)

done

Answer 5

1 / (x + 1/y) =

1 / ((xy + 1)/y) =

y / (xy + 1)