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

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

Procijeni

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

Kratki koraci rješenja

Faktorirajte izraze koji nisu već faktorirani u \frac{2y-6}{y^{2}-9}.

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

Otkaži y-3 u brojiocu i imeniocu.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva y+3 i y-1 je \left(y-1\right)\left(y+3\right). Pomnožite \frac{2}{y+3} i \frac{y-1}{y-1}. Pomnožite \frac{y}{y-1} i \frac{y+3}{y+3}.

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

Pošto \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} i \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u 2\left(y-1\right)-y\left(y+3\right).

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

Kombinirajte slične izraze u 2y-2-y^{2}-3y.

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

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

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

Pošto \frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} i \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Kombinirajte slične izraze u -y-2-y^{2}+y^{2}+2.

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

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

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

Proširi

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

Kratki koraci rješenja

Faktorirajte izraze koji nisu već faktorirani u \frac{2y-6}{y^{2}-9}.

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

Otkaži y-3 u brojiocu i imeniocu.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva y+3 i y-1 je \left(y-1\right)\left(y+3\right). Pomnožite \frac{2}{y+3} i \frac{y-1}{y-1}. Pomnožite \frac{y}{y-1} i \frac{y+3}{y+3}.

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

Pošto \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} i \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u 2\left(y-1\right)-y\left(y+3\right).

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

Kombinirajte slične izraze u 2y-2-y^{2}-3y.

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

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

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

Pošto \frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} i \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Kombinirajte slične izraze u -y-2-y^{2}+y^{2}+2.

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

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

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