Issolvi 2/x+5/x+1=

$$\frac { 2 } { x } + \frac { 5 } { x + 1 } =$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

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

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

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

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

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

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

Ikkombina termini simili f'2x+2+5x.

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

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

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

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

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

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

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

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

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

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

Ikkombina termini simili f'2x+2+5x.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x+2}{x^{2}+x})$$

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.

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

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}.

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

Issimplifika.

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

Immultiplika x^{2}+x^{1} b'7x^{0}.

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

Immultiplika 7x^{1}+2 b'2x^{1}+x^{0}.

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

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

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

Issimplifika.

$$\frac{7x^{2}+7x^{1}-\left(14x^{2}+7x^{1}+4x^{1}+2x^{0}\right)}{\left(x^{2}+x^{1}\right)^{2}}$$

Ikkombina termini simili.

$$\frac{-7x^{2}-4x^{1}-2x^{0}}{\left(x^{2}+x^{1}\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{-7x^{2}-4x-2x^{0}}{\left(x^{2}+x\right)^{2}}$$

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

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