Rešite 4*6/x^2-4x+3-3/3-x-4/x-1

$$\frac { 4 \times 6 } { x ^ { 2 } - 4 x + 3 } - \frac { 3 } { 3 - x } - \frac { 4 } { x - 1 }$$

Ovrednoti

$$\frac{x-33}{\left(3-x\right)\left(x-1\right)}$$

Kratka navodila za rešitev

Pomnožite 4 in 6, da dobite 24.

$$\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1}$$

Faktorizirajte x^{2}-4x+3.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-1\right) in 3-x je \left(x-3\right)\left(x-1\right). Pomnožite \frac{3}{3-x} s/z \frac{-\left(x-1\right)}{-\left(x-1\right)}.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Ker \frac{24}{\left(x-3\right)\left(x-1\right)} in \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Izvedi množenje v 24-3\left(-1\right)\left(x-1\right).

$$\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Združite podobne člene v 24+3x-3.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-1\right) in x-1 je \left(x-3\right)\left(x-1\right). Pomnožite \frac{4}{x-1} s/z \frac{x-3}{x-3}.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Ker \frac{21+3x}{\left(x-3\right)\left(x-1\right)} in \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

Izvedi množenje v 21+3x-4\left(x-3\right).

$$\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)}$$

Združite podobne člene v 21+3x-4x+12.

$$\frac{33-x}{\left(x-3\right)\left(x-1\right)}$$

Razčlenite \left(x-3\right)\left(x-1\right).

$$\frac{33-x}{x^{2}-4x+3}$$

Odvajajte w.r.t. x

$$\frac{x^{2}-66x+129}{x^{4}-8x^{3}+22x^{2}-24x+9}$$

Koraki z uporabo pravila odvoda za kvocient

Pomnožite 4 in 6, da dobite 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1})$$

Faktorizirajte x^{2}-4x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1})$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-1\right) in 3-x je \left(x-3\right)\left(x-1\right). Pomnožite \frac{3}{3-x} s/z \frac{-\left(x-1\right)}{-\left(x-1\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Ker \frac{24}{\left(x-3\right)\left(x-1\right)} in \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Izvedi množenje v 24-3\left(-1\right)\left(x-1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Združite podobne člene v 24+3x-3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-1\right) in x-1 je \left(x-3\right)\left(x-1\right). Pomnožite \frac{4}{x-1} s/z \frac{x-3}{x-3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Ker \frac{21+3x}{\left(x-3\right)\left(x-1\right)} in \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

Izvedi množenje v 21+3x-4\left(x-3\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)})$$

Združite podobne člene v 21+3x-4x+12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{\left(x-3\right)\left(x-1\right)})$$

Uporabite lastnost distributivnosti za množenje x-3 krat x-1 in kombiniranje pogojev podobnosti.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{x^{2}-4x+3})$$

Za kateri koli dve odvedljivi funkciji je odvod kvocienta dveh funkcij imenovalec krat odvod števca minus števec krat odvod imenovalca, vse skupaj pa je deljeno s kvadratom imenovalca.

$$\frac{\left(x^{2}-4x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+33)-\left(-x^{1}+33\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}+3)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Odvod polinoma je vsota odvodov njegovih členov. Odvod katerega koli prostega člena je 0. Odvod člena ax^{n} je nax^{n-1}.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{1-1}-\left(-x^{1}+33\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Poenostavite.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Pomnožite x^{2}-4x^{1}+3 s/z -x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Pomnožite -x^{1}+33 s/z 2x^{1}-4x^{0}.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-4\right)x^{0}+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Če želite množiti potence iste osnove, seštejte njihove eksponente.

$$\frac{-x^{2}-4\left(-1\right)x^{1}+3\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-4x^{1}\right)+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Poenostavite.

$$\frac{-x^{2}+4x^{1}-3x^{0}-\left(-2x^{2}+4x^{1}+66x^{1}-132x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Združite podobne člene.

$$\frac{x^{2}-66x^{1}+129x^{0}}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Za kakršen koli izraz t, t^{1}=t.

$$\frac{x^{2}-66x+129x^{0}}{\left(x^{2}-4x+3\right)^{2}}$$

Za kakršen koli izraz t, razen 0, t^{0}=1.

$$\frac{x^{2}-66x+129\times 1}{\left(x^{2}-4x+3\right)^{2}}$$

Za kakršen koli izraz t, t\times 1=t in 1t=t.

$$\frac{x^{2}-66x+129}{\left(x^{2}-4x+3\right)^{2}}$$