How do you simplify #(x/y - y/x)/(1/y + 1/x)# and can you use a calculator to simplify?

Question

Avery Alexander · Accepted Answer

#color(red)"The answer is (x-y)"#

#{(x/y)-(y/x)}/{(1/x)-(1/y)}#

On further solving this problem we get,

#{(x^2-y^2)/(xy)}/{(x+y)/(xy)}#

Now dividing both the sides we get, #xy# as cancelled from both the numerator and denominator.

#{(x+y)(x-y)}/(x+y)#

Cancelling #x+y# from both numerator and denominator we get,

Ans. = #(x-y)#

Eva Abramson · Answer

Looking at the numerator

#x/y-y/x# if we put them over a common denominator

#(x^2-y^2)/(xy)#

Now looking at the denominator

#1/y+1/x# and put this over a common denominator

#(x+y)/(xy)#

So we have

#[(x^2-y^2)/(xy)]/[(x+y)/(xy)]#

#(x^2-y^2)/(xy)xx(xy)/(x+y)#

#(x^2-y^2)/(x+y)#

#[(x+y)(x-y)]/(x+y)#

#x-y#

Avery Alexander · Answer

undefined To simplify the expression (x/y - y/x)/(1/y + 1/x), we can start by finding a common denominator for the fractions. The common denominator is xy.

(x/y - y/x)/(1/y + 1/x) simplifies to ((x^2 - y^2)/(xy))/(x + y)/(xy).

Next, we can simplify further by multiplying the numerator by the reciprocal of the denominator.

((x^2 - y^2)/(xy))/(x + y)/(xy) simplifies to (x^2 - y^2)/(xy) * (xy)/(x + y).

The xy terms cancel out, leaving us with (x^2 - y^2)/(x + y).

No, a calculator cannot simplify this expression as it requires algebraic manipulation.