Issolvi a^5/a-1-a^2/a+1-1/a-1+1/a+1

$$\frac { a ^ { 5 } } { a - 1 } - \frac { a ^ { 2 } } { a + 1 } - \frac { 1 } { a - 1 } + \frac { 1 } { a + 1 }$$

Evalwa

$$a^{4}+a^{3}+a^{2}+2$$

Passi Qosra tas-Soluzzjonijiet

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

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

Billi \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} u \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1}$$

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

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{a+1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Billi \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} u \frac{a+1}{\left(a-1\right)\left(a+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Agħmel il-multiplikazzjonijiet fi a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

$$\frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

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

$$\frac{\left(a-1\right)\left(a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1}$$

Annulla a-1 fin-numeratur u d-denominatur.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1}+\frac{1}{a+1}$$

Billi \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} u \frac{1}{a+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1}{a+1}$$

Ikkombina termini simili f'a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

$$\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Annulla a+1 fin-numeratur u d-denominatur.

$$\left(a^{2}-a+1\right)\left(a^{2}+2a+2\right)$$

Espandi l-espressjoni.

$$a^{4}+a^{3}+a^{2}+2$$

Iddifferenzja w.r.t. a

$$a\left(4a^{2}+3a+2\right)$$

Passi għall-Użu ta' Regola Derivattiva għal Somma

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

Billi \frac{a^{5}\left(a+1\right)}{\left(a-1\right)\left(a+1\right)} u \frac{a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}\left(a+1\right)-a^{2}\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

Agħmel il-multiplikazzjonijiet fi a^{5}\left(a+1\right)-a^{2}\left(a-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{1}{a-1}+\frac{1}{a+1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)}-\frac{a+1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Billi \frac{a^{6}+a^{5}-a^{3}+a^{2}}{\left(a-1\right)\left(a+1\right)} u \frac{a+1}{\left(a-1\right)\left(a+1\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Agħmel il-multiplikazzjonijiet fi a^{6}+a^{5}-a^{3}+a^{2}-\left(a+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{6}+a^{5}-a^{3}+a^{2}-a-1}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\left(a-1\right)\left(a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1\right)}{\left(a-1\right)\left(a+1\right)}+\frac{1}{a+1})$$

Annulla a-1 fin-numeratur u d-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1}+\frac{1}{a+1})$$

Billi \frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1}{a+1} u \frac{1}{a+1} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1}{a+1})$$

Ikkombina termini simili f'a^{5}+2a^{4}+2a^{3}+a^{2}+2a+1+1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1})$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{a^{5}+2a^{4}+2a^{3}+a^{2}+2a+2}{a+1}.

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

Annulla a+1 fin-numeratur u d-denominatur.

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

Espandi l-espressjoni.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}+a^{3}+a^{2}+2)$$

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}.

$$4a^{4-1}+3a^{3-1}+2a^{2-1}$$

Naqqas 1 minn 4.

$$4a^{3}+3a^{3-1}+2a^{2-1}$$

Naqqas 1 minn 3.

$$4a^{3}+3a^{2}+2a^{2-1}$$

Naqqas 1 minn 2.

$$4a^{3}+3a^{2}+2a^{1}$$

Għal kwalunkwe terminu t, t^{1}=t.

$$4a^{3}+3a^{2}+2a$$