How do you simplify $\frac{\frac{x}{y} - \frac{y}{x}}{\frac{1}{y} + \frac{1}{x}}$ $(x/y - y/x)/(1/y + 1/x)$ and can you use a calculator to simplify?

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Answer 1 · 2018-07-04T06:47:07

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

$\frac{(\frac{x}{y}) - (\frac{y}{x})}{(\frac{1}{x}) - (\frac{1}{y})}$ ${(x/y)-(y/x)}/{(1/x)-(1/y)}$

On further solving this problem we get,

$\frac{\frac{x^{2} - y^{2}}{x y}}{\frac{x + y}{x y}}$ ${(x^2-y^2)/(xy)}/{(x+y)/(xy)}$

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

$\frac{(x + y) (x - y)}{x + y}$ ${(x+y)(x-y)}/(x+y)$

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

Ans. = $(x - y)$ $(x-y)$

Answer 2 · 2018-07-04T06:58:56

Looking at the numerator

$\frac{x}{y} - \frac{y}{x}$ $x/y-y/x$ if we put them over a common denominator

$\frac{x^{2} - y^{2}}{x y}$ $(x^2-y^2)/(xy)$

Now looking at the denominator

$\frac{1}{y} + \frac{1}{x}$ $1/y+1/x$ and put this over a common denominator

$\frac{x + y}{x y}$ $(x+y)/(xy)$

So we have

$\frac{\frac{x^{2} - y^{2}}{x y}}{\frac{x + y}{x y}}$ $[(x^2-y^2)/(xy)]/[(x+y)/(xy)]$

$\frac{x^{2} - y^{2}}{x y} \times \frac{x y}{x + y}$ $(x^2-y^2)/(xy)xx(xy)/(x+y)$

$\frac{x^{2} - y^{2}}{x + y}$ $(x^2-y^2)/(x+y)$

$\frac{(x + y) (x - y)}{x + y}$ $[(x+y)(x-y)]/(x+y)$

$x - y$ $x-y$

How do you simplify xy−yx1y+1x(x/y - y/x)/(1/y + 1/x) and can you use a calculator to simplify?