Issolvi f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

Evalwa

$$\frac{3}{x-1}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Annulla x+3 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

Annulla x+1 fin-numeratur u d-denominatur.

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

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

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

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

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

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

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

Ikkombina termini simili f'x^{2}+2x+x+2-x^{2}+x-x+1.

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

Immultiplika \frac{3x+3}{\left(x-1\right)\left(x+2\right)} b'\frac{x+2}{x+1} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla x+2 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

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

Annulla x+1 fin-numeratur u d-denominatur.

$$\frac{3}{x-1}$$

Espandi

$$\frac{3}{x-1}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Annulla x+3 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

Annulla x+1 fin-numeratur u d-denominatur.

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

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

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

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

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

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

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

Ikkombina termini simili f'x^{2}+2x+x+2-x^{2}+x-x+1.

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

Immultiplika \frac{3x+3}{\left(x-1\right)\left(x+2\right)} b'\frac{x+2}{x+1} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla x+2 fin-numeratur u d-denominatur.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

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

Annulla x+1 fin-numeratur u d-denominatur.

$$\frac{3}{x-1}$$