Issolvi 1/x^2+4x+3+1/x^2+8x+15+1/x^2+12x+35

$$\frac { 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 1 } { x ^ { 2 } + 8 x + 15 } + \frac { 1 } { x ^ { 2 } + 12 x + 35 }$$

Evalwa

$$\frac{3}{\left(x+1\right)\left(x+7\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{2}+4x+3. Iffattura x^{2}+8x+15.

$$\frac{1}{\left(x+1\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

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

$$\frac{x+5}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

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

$$\frac{x+5+x+1}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Ikkombina termini simili f'x+5+x+1.

$$\frac{2x+6}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{2x+6}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}.

$$\frac{2\left(x+3\right)}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

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

$$\frac{2}{\left(x+1\right)\left(x+5\right)}+\frac{1}{x^{2}+12x+35}$$

Iffattura x^{2}+12x+35.

$$\frac{2}{\left(x+1\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+7\right)}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x+1\right)\left(x+5\right) u \left(x+5\right)\left(x+7\right) huwa \left(x+1\right)\left(x+5\right)\left(x+7\right). Immultiplika \frac{2}{\left(x+1\right)\left(x+5\right)} b'\frac{x+7}{x+7}. Immultiplika \frac{1}{\left(x+5\right)\left(x+7\right)} b'\frac{x+1}{x+1}.

$$\frac{2\left(x+7\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}+\frac{x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Billi \frac{2\left(x+7\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)} u \frac{x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2\left(x+7\right)+x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Agħmel il-multiplikazzjonijiet fi 2\left(x+7\right)+x+1.

$$\frac{2x+14+x+1}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Ikkombina termini simili f'2x+14+x+1.

$$\frac{3x+15}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{3x+15}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}.

$$\frac{3\left(x+5\right)}{\left(x+1\right)\left(x+5\right)\left(x+7\right)}$$

Annulla x+5 fin-numeratur u d-denominatur.

$$\frac{3}{\left(x+1\right)\left(x+7\right)}$$

Espandi \left(x+1\right)\left(x+7\right).

$$\frac{3}{x^{2}+8x+7}$$

Iddifferenzja w.r.t. x

$$\frac{6\left(-x-4\right)}{\left(\left(x+1\right)\left(x+7\right)\right)^{2}}$$