Los xleft(y-1right)+yleft(1-xright)/left(x-1right)left(1-yright)-y-x/(x-1)(y-1) op

$$\frac{ x \left( y-1 \right) +y \left( 1-x \right) }{ \left( x-1 \right) \left( 1-y \right) } - \frac{ y-x }{ (x-1)(y-1) }$$

Evalueren

$$\frac{2\left(y-x\right)}{\left(1-y\right)\left(x-1\right)}$$

Korte oplossingsstappen

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Kleinste gemene veelvoud van \left(x-1\right)\left(1-y\right) en \left(x-1\right)\left(y-1\right) is \left(x-1\right)\left(y-1\right). Vermenigvuldig \frac{x\left(y-1\right)+y\left(1-x\right)}{\left(x-1\right)\left(1-y\right)} met \frac{-1}{-1}.

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)}-\frac{y-x}{\left(x-1\right)\left(y-1\right)}$$

Aangezien \frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)} en \frac{y-x}{\left(x-1\right)\left(y-1\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

Voer de vermenigvuldigingen uit in -\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right).

$$\frac{-yx+x-y+yx-y+x}{\left(x-1\right)\left(y-1\right)}$$

Combineer gelijke termen in -yx+x-y+yx-y+x.

$$\frac{2x-2y}{\left(x-1\right)\left(y-1\right)}$$

Breid \left(x-1\right)\left(y-1\right) uit.

$$\frac{2x-2y}{xy-x-y+1}$$

Uitbreiden

$$-\frac{2\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

Korte oplossingsstappen

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Kleinste gemene veelvoud van \left(x-1\right)\left(1-y\right) en \left(x-1\right)\left(y-1\right) is \left(x-1\right)\left(y-1\right). Vermenigvuldig \frac{x\left(y-1\right)+y\left(1-x\right)}{\left(x-1\right)\left(1-y\right)} met \frac{-1}{-1}.

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)}-\frac{y-x}{\left(x-1\right)\left(y-1\right)}$$

Aangezien \frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)}{\left(x-1\right)\left(y-1\right)} en \frac{y-x}{\left(x-1\right)\left(y-1\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

$$\frac{-\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right)}{\left(x-1\right)\left(y-1\right)}$$

Voer de vermenigvuldigingen uit in -\left(x\left(y-1\right)+y\left(1-x\right)\right)-\left(y-x\right).

$$\frac{-yx+x-y+yx-y+x}{\left(x-1\right)\left(y-1\right)}$$

Combineer gelijke termen in -yx+x-y+yx-y+x.

$$\frac{2x-2y}{\left(x-1\right)\left(y-1\right)}$$

Breid \left(x-1\right)\left(y-1\right) uit.

$$\frac{2x-2y}{xy-x-y+1}$$