Rešite 2y-6/y^2-9-y/y-1+y^2+2/y^2+2y-3

$$\frac { 2 y - 6 } { y ^ { 2 } - 9 } - \frac { y } { y - 1 } + \frac { y ^ { 2 } + 2 } { y ^ { 2 } + 2 y - 3 }$$

Ovrednoti

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

Kratka navodila za rešitev

Faktorizirajte izraze, ki še niso faktorizirani v \frac{2y-6}{y^{2}-9}.

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

Okrajšaj y-3 v števcu in imenovalcu.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik y+3 in y-1 je \left(y-1\right)\left(y+3\right). Pomnožite \frac{2}{y+3} s/z \frac{y-1}{y-1}. Pomnožite \frac{y}{y-1} s/z \frac{y+3}{y+3}.

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

Ker \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} in \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v 2\left(y-1\right)-y\left(y+3\right).

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

Združite podobne člene v 2y-2-y^{2}-3y.

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

Faktorizirajte y^{2}+2y-3.

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

\frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} in \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Združite podobne člene v -y-2-y^{2}+y^{2}+2.

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

Razčlenite \left(y-1\right)\left(y+3\right).

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

Razširi

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

Kratka navodila za rešitev

Faktorizirajte izraze, ki še niso faktorizirani v \frac{2y-6}{y^{2}-9}.

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

Okrajšaj y-3 v števcu in imenovalcu.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik y+3 in y-1 je \left(y-1\right)\left(y+3\right). Pomnožite \frac{2}{y+3} s/z \frac{y-1}{y-1}. Pomnožite \frac{y}{y-1} s/z \frac{y+3}{y+3}.

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

Ker \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} in \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v 2\left(y-1\right)-y\left(y+3\right).

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

Združite podobne člene v 2y-2-y^{2}-3y.

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

Faktorizirajte y^{2}+2y-3.

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

\frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} in \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Združite podobne člene v -y-2-y^{2}+y^{2}+2.

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

Razčlenite \left(y-1\right)\left(y+3\right).

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