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

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{2y-6}{y^{2}-9}.

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

Annulla y-3 fin-numeratur u d-denominatur.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' y+3 u y-1 huwa \left(y-1\right)\left(y+3\right). Immultiplika \frac{2}{y+3} b'\frac{y-1}{y-1}. Immultiplika \frac{y}{y-1} b'\frac{y+3}{y+3}.

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

Billi \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} u \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 2\left(y-1\right)-y\left(y+3\right).

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

Ikkombina termini simili f'2y-2-y^{2}-3y.

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

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

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

Billi \frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} u \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Ikkombina termini simili f'-y-2-y^{2}+y^{2}+2.

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

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

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

Espandi

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

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{2y-6}{y^{2}-9}.

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

Annulla y-3 fin-numeratur u d-denominatur.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' y+3 u y-1 huwa \left(y-1\right)\left(y+3\right). Immultiplika \frac{2}{y+3} b'\frac{y-1}{y-1}. Immultiplika \frac{y}{y-1} b'\frac{y+3}{y+3}.

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

Billi \frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} u \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 2\left(y-1\right)-y\left(y+3\right).

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

Ikkombina termini simili f'2y-2-y^{2}-3y.

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

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

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

Billi \frac{-y-2-y^{2}}{\left(y-1\right)\left(y+3\right)} u \frac{y^{2}+2}{\left(y-1\right)\left(y+3\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Ikkombina termini simili f'-y-2-y^{2}+y^{2}+2.

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

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

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