Issolvi (x+2)-4/x-1

$$(x+2)- \frac{ 4 }{ x-1 }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika x+2 b'\frac{x-1}{x-1}.

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

Billi \frac{\left(x+2\right)\left(x-1\right)}{x-1} u \frac{4}{x-1} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi \left(x+2\right)\left(x-1\right)-4.

$$\frac{x^{2}-x+2x-2-4}{x-1}$$

Ikkombina termini simili f'x^{2}-x+2x-2-4.

$$\frac{x^{2}+x-6}{x-1}$$

Iddifferenzja w.r.t. x

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

Passi għall-Użu ta' Regola Derivattiva għal Kwozjent

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika x+2 b'\frac{x-1}{x-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x+2\right)\left(x-1\right)}{x-1}-\frac{4}{x-1})$$

Billi \frac{\left(x+2\right)\left(x-1\right)}{x-1} u \frac{4}{x-1} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x+2\right)\left(x-1\right)-4}{x-1})$$

Agħmel il-multiplikazzjonijiet fi \left(x+2\right)\left(x-1\right)-4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-x+2x-2-4}{x-1})$$

Ikkombina termini simili f'x^{2}-x+2x-2-4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+x-6}{x-1})$$

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.

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

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}.

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

Issimplifika.

$$\frac{\left(x^{1}-1\right)\left(2x^{1}+x^{0}\right)-\left(x^{2}+x^{1}-6\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{x^{1}\times 2x^{1}+x^{1}x^{0}-2x^{1}-x^{0}-\left(x^{2}+x^{1}-6\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

Immultiplika x^{2}+x^{1}-6 b'x^{0}.

$$\frac{x^{1}\times 2x^{1}+x^{1}x^{0}-2x^{1}-x^{0}-\left(x^{2}x^{0}+x^{1}x^{0}-6x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{2x^{1+1}+x^{1}-2x^{1}-x^{0}-\left(x^{2}+x^{1}-6x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Issimplifika.

$$\frac{2x^{2}+x^{1}-2x^{1}-x^{0}-\left(x^{2}+x^{1}-6x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Ikkombina termini simili.

$$\frac{x^{2}-2x^{1}+5x^{0}}{\left(x^{1}-1\right)^{2}}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$\frac{x^{2}-2x+5x^{0}}{\left(x-1\right)^{2}}$$

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

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

Għal kwalunkwe terminu t, t\times 1=t u 1t=t.

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