Rešite (x/y+1-x/y-1)x+xy^2/3x^2

$$( \frac{ x }{ y+1 } - \frac{ x }{ y-1 } ) \frac{ x+x { y }^{ 2 } }{ 3 { x }^{ 2 } }$$

Ovrednoti

$$-\frac{2\left(y^{2}+1\right)}{3\left(y^{2}-1\right)}$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik y+1 in y-1 je \left(y-1\right)\left(y+1\right). Pomnožite \frac{x}{y+1} s/z \frac{y-1}{y-1}. Pomnožite \frac{x}{y-1} s/z \frac{y+1}{y+1}.

$$\left(\frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}-\frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\right)\times \frac{x+xy^{2}}{3x^{2}}$$

Ker \frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)} in \frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{x\left(y-1\right)-x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Izvedi množenje v x\left(y-1\right)-x\left(y+1\right).

$$\frac{xy-x-xy-x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Združite podobne člene v xy-x-xy-x.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x+xy^{2}}{3x^{2}}.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x\left(y^{2}+1\right)}{3x^{2}}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{y^{2}+1}{3x}$$

Pomnožite \frac{-2x}{\left(y-1\right)\left(y+1\right)} s/z \frac{y^{2}+1}{3x} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{-2x\left(y^{2}+1\right)}{\left(y-1\right)\left(y+1\right)\times 3x}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{-2\left(y^{2}+1\right)}{3\left(y-1\right)\left(y+1\right)}$$

Uporabite distributivnost, da pomnožite -2 s/z y^{2}+1.

$$\frac{-2y^{2}-2}{3\left(y-1\right)\left(y+1\right)}$$

Uporabite distributivnost, da pomnožite 3 s/z y-1.

$$\frac{-2y^{2}-2}{\left(3y-3\right)\left(y+1\right)}$$

Uporabite lastnost distributivnosti za množenje 3y-3 krat y+1 in kombiniranje pogojev podobnosti.

$$\frac{-2y^{2}-2}{3y^{2}-3}$$

Razširi

$$-\frac{2\left(y^{2}+1\right)}{3\left(y^{2}-1\right)}$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik y+1 in y-1 je \left(y-1\right)\left(y+1\right). Pomnožite \frac{x}{y+1} s/z \frac{y-1}{y-1}. Pomnožite \frac{x}{y-1} s/z \frac{y+1}{y+1}.

$$\left(\frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)}-\frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\right)\times \frac{x+xy^{2}}{3x^{2}}$$

Ker \frac{x\left(y-1\right)}{\left(y-1\right)\left(y+1\right)} in \frac{x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{x\left(y-1\right)-x\left(y+1\right)}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Izvedi množenje v x\left(y-1\right)-x\left(y+1\right).

$$\frac{xy-x-xy-x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Združite podobne člene v xy-x-xy-x.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x+xy^{2}}{3x^{2}}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x+xy^{2}}{3x^{2}}.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{x\left(y^{2}+1\right)}{3x^{2}}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{-2x}{\left(y-1\right)\left(y+1\right)}\times \frac{y^{2}+1}{3x}$$

Pomnožite \frac{-2x}{\left(y-1\right)\left(y+1\right)} s/z \frac{y^{2}+1}{3x} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{-2x\left(y^{2}+1\right)}{\left(y-1\right)\left(y+1\right)\times 3x}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{-2\left(y^{2}+1\right)}{3\left(y-1\right)\left(y+1\right)}$$

Uporabite distributivnost, da pomnožite -2 s/z y^{2}+1.

$$\frac{-2y^{2}-2}{3\left(y-1\right)\left(y+1\right)}$$

Uporabite distributivnost, da pomnožite 3 s/z y-1.

$$\frac{-2y^{2}-2}{\left(3y-3\right)\left(y+1\right)}$$

Uporabite lastnost distributivnosti za množenje 3y-3 krat y+1 in kombiniranje pogojev podobnosti.

$$\frac{-2y^{2}-2}{3y^{2}-3}$$