Issolvi 5/(x+1)-2/17-3

$$\frac { 5 } { ( x + 1 ) } - \frac { 2 } { 17 - 3 }$$

Evalwa

$$\frac{34-x}{7\left(x+1\right)}$$

Passi Qosra tas-Soluzzjonijiet

Naqqas 3 minn 17 biex tikseb 14.

$$\frac{5}{x+1}-\frac{2}{14}$$

Naqqas il-frazzjoni \frac{2}{14} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{5}{x+1}-\frac{1}{7}$$

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

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

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

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

Agħmel il-multiplikazzjonijiet fi 5\times 7-\left(x+1\right).

$$\frac{35-x-1}{7\left(x+1\right)}$$

Ikkombina termini simili f'35-x-1.

$$\frac{34-x}{7\left(x+1\right)}$$

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

$$\frac{34-x}{7x+7}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Naqqas 3 minn 17 biex tikseb 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{x+1}-\frac{2}{14})$$

Naqqas il-frazzjoni \frac{2}{14} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{x+1}-\frac{1}{7})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7}{7\left(x+1\right)}-\frac{x+1}{7\left(x+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7-\left(x+1\right)}{7\left(x+1\right)})$$

Agħmel il-multiplikazzjonijiet fi 5\times 7-\left(x+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35-x-1}{7\left(x+1\right)})$$

Ikkombina termini simili f'35-x-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{34-x}{7\left(x+1\right)})$$

Uża l-propjetà distributtiva biex timmultiplika 7 b'x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{34-x}{7x+7})$$

Għal kwalunkwe żewġ funzjonijiet differenzjabbli, id-derivattiv tal-kwozjent ta' żewġ funzjonijiet huwa d-denominatur immultiplikat bid-derivattiv tan-numeratur minus in-numeratur immultiplikat bid-derivattiv tad-denominatur, kollha diviżi bid-denominatur kwadrat.

$$\frac{\left(7x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+34)-\left(-x^{1}+34\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}+7)}{\left(7x^{1}+7\right)^{2}}$$

Id-derivattiva ta’ polynomial hija s-somma tad-derivattivi tat-termini tagħha. Id-derivattiva ta’ terminu kostanti hija 0. Id-derivattiva ta’ ax^{n} hijanax^{n-1}.

$$\frac{\left(7x^{1}+7\right)\left(-1\right)x^{1-1}-\left(-x^{1}+34\right)\times 7x^{1-1}}{\left(7x^{1}+7\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{\left(7x^{1}+7\right)\left(-1\right)x^{0}-\left(-x^{1}+34\right)\times 7x^{0}}{\left(7x^{1}+7\right)^{2}}$$

Espandi bl-użu ta' propjetà distributtiva.

$$\frac{7x^{1}\left(-1\right)x^{0}+7\left(-1\right)x^{0}-\left(-x^{1}\times 7x^{0}+34\times 7x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom.

$$\frac{7\left(-1\right)x^{1}+7\left(-1\right)x^{0}-\left(-7x^{1}+34\times 7x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

Agħmel l-aritmetika.

$$\frac{-7x^{1}-7x^{0}-\left(-7x^{1}+238x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

Neħħi l-parenteżi mhux meħtieġa.

$$\frac{-7x^{1}-7x^{0}-\left(-7x^{1}\right)-238x^{0}}{\left(7x^{1}+7\right)^{2}}$$

Ikkombina termini simili.

$$\frac{\left(-7-\left(-7\right)\right)x^{1}+\left(-7-238\right)x^{0}}{\left(7x^{1}+7\right)^{2}}$$

Naqqas -7 minn -7 u 238 minn -7.

$$\frac{-245x^{0}}{\left(7x^{1}+7\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{-245x^{0}}{\left(7x+7\right)^{2}}$$

Għal kwalunkwe terminu t ħlief 0, t^{0}=1.

$$\frac{-245}{\left(7x+7\right)^{2}}$$