Issolvi 1/x^2-5x+6+1/x^2-3x+2+2/x^2-8x+15

$$\frac { 1 } { x ^ { 2 } - 5 x + 6 } + \frac { 1 } { x ^ { 2 } - 3 x + 2 } + \frac { 2 } { x ^ { 2 } - 8 x + 15 }$$

Evalwa

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{2}-5x+6. Iffattura x^{2}-3x+2.

$$\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1+x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Ikkombina termini simili f'x-1+x-3.

$$\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}.

$$\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Iffattura x^{2}-8x+15.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{\left(x-5\right)\left(x-3\right)}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x-3\right)\left(x-1\right) u \left(x-5\right)\left(x-3\right) huwa \left(x-5\right)\left(x-3\right)\left(x-1\right). Immultiplika \frac{2}{\left(x-3\right)\left(x-1\right)} b'\frac{x-5}{x-5}. Immultiplika \frac{2}{\left(x-5\right)\left(x-3\right)} b'\frac{x-1}{x-1}.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}+\frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Billi \frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} u \frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2\left(x-5\right)+2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Agħmel il-multiplikazzjonijiet fi 2\left(x-5\right)+2\left(x-1\right).

$$\frac{2x-10+2x-2}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Ikkombina termini simili f'2x-10+2x-2.

$$\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}.

$$\frac{4\left(x-3\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

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

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Espandi \left(x-5\right)\left(x-1\right).

$$\frac{4}{x^{2}-6x+5}$$

Iddifferenzja w.r.t. x

$$\frac{8\left(3-x\right)}{\left(\left(x-5\right)\left(x-1\right)\right)^{2}}$$