Can you please answer this question because i am getting lost ...
$\displaystyle \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz} $
Can you please answer this question because i am getting lost ...
$\displaystyle \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz} $
You can also follow
$\displaystyle
=\frac{x}{xy} - \frac{y}{xy} + \frac{x}{xz} +\frac{-z}{xz} - \frac{z}{yz} - \frac{-y}{yz}
$
Now see if anything gets cancelled in
$\displaystyle
=\frac{1}{y} - \frac{1}{x} + \frac{1}{z} +\frac{-1}{x} - \frac{1}{y} - \frac{-1}{z}
$
One more thing its always better to ask different questions in different threads
Helli, mj.alawami!
$\displaystyle \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz} $
The LCD is $\displaystyle xyz$
We must "convert" each fraction so they all have the LCD.
. . We multiply each fraction by an appropriate fraction.
$\displaystyle {\color{blue}\frac{z}{z}}\cdot\frac{x-y}{xy} + {\color{blue}\frac{y}{y}}\cdot\frac{x-z}{xz} - {\color{blue}\frac{x}{x}}\cdot\frac{z-y}{yz}$
. . $\displaystyle = \;\frac{z(x-y)}{xyz} + \frac{y(x-z)}{xyz} - \frac{x(z-y)}{xyz}$ . They have the same denominator.
. . $\displaystyle = \;\frac{z(x-y) + y(x-z) - x(z-y)}{xyz}$ . We can make one big fraction.
. . $\displaystyle = \;\frac{xz - yz + xy - yz - xz + xy}{xyz}$ . Simplify the numerator, factor, and reduce.
. . $\displaystyle = \;\frac{2xy - 2yz}{xyz} \;=\;\frac{2{\color{red}\rlap{/}}y(x-z)}{x{\color{red}\rlap{/}}yz} \;=\;\frac{2(x-z)}{xz} $