Rešite [1.5-(x^{4}-frac{x^{4}+1}{x^{2}+1})*frac{(x^{2}+1)(x-4)}{x^7+6x^6-x-6}]:x^2+29x+78/3x^2+12x-36=

$$[ 1.5 - ( x ^ { 4 } - \frac { x ^ { 4 } + 1 } { x ^ { 2 } + 1 } ) \cdot \frac { ( x ^ { 2 } + 1 ) ( x - 4 ) } { x ^ { 7 } + 6 x ^ { 6 } - x - 6 } ] : \frac { x ^ { 2 } + 29 x + 78 } { 3 x ^ { 2 } + 12 x - 36 } =$$

Ovrednoti

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite x^{4} s/z \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1,5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Ker \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} in \frac{x^{4}+1}{x^{2}+1} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{1,5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Izvedi množenje v x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1,5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Združite podobne člene v x^{6}+x^{4}-x^{4}-1.

$$\frac{1,5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Pomnožite \frac{x^{6}-1}{x^{2}+1} s/z \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{1,5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Okrajšaj x^{2}+1 v števcu in imenovalcu.

$$\frac{1,5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1,5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Okrajšaj \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) v števcu in imenovalcu.

$$\frac{1,5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Delite 1,5-\frac{x-4}{x+6} s/z \frac{x^{2}+29x+78}{3x^{2}+12x-36} tako, da pomnožite 1,5-\frac{x-4}{x+6} z obratno vrednostjo \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1,5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Uporabite distributivnost, da pomnožite 1,5-\frac{x-4}{x+6} s/z 3x^{2}+12x-36.

$$\frac{4,5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite -3\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite \frac{-3\left(x-4\right)}{x+6}x^{2} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite -12\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite \frac{-12\left(x-4\right)}{x+6}x kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite 36\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite 18x-54 s/z \frac{x+6}{x+6}.

$$\frac{4,5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{\left(18x-54\right)\left(x+6\right)}{x+6} in \frac{-3\left(x-4\right)x^{2}}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4,5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{30x^{2}+54x-324-3x^{3}}{x+6} in \frac{-12\left(x-4\right)x}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{18x^{2}+102x-324-3x^{3}}{x+6} in \frac{36\left(x-4\right)}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4,5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4,5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Okrajšaj x+6 v števcu in imenovalcu.

$$\frac{4,5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Razširite izraz.

$$\frac{4,5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Združite 4,5x^{2} in -3x^{2}, da dobite 1,5x^{2}.

$$\frac{1,5x^{2}+36x-78}{x^{2}+29x+78}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Okrajšaj x+26 v števcu in imenovalcu.

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

Razširite izraz.

$$\frac{\frac{3}{2}x-3}{x+3}$$

Razširi

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite x^{4} s/z \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1,5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Ker \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} in \frac{x^{4}+1}{x^{2}+1} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{1,5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Izvedi množenje v x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1,5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Združite podobne člene v x^{6}+x^{4}-x^{4}-1.

$$\frac{1,5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Pomnožite \frac{x^{6}-1}{x^{2}+1} s/z \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{1,5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Okrajšaj x^{2}+1 v števcu in imenovalcu.

$$\frac{1,5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1,5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Okrajšaj \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) v števcu in imenovalcu.

$$\frac{1,5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Delite 1,5-\frac{x-4}{x+6} s/z \frac{x^{2}+29x+78}{3x^{2}+12x-36} tako, da pomnožite 1,5-\frac{x-4}{x+6} z obratno vrednostjo \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1,5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Uporabite distributivnost, da pomnožite 1,5-\frac{x-4}{x+6} s/z 3x^{2}+12x-36.

$$\frac{4,5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite -3\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite \frac{-3\left(x-4\right)}{x+6}x^{2} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite -12\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite \frac{-12\left(x-4\right)}{x+6}x kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Izrazite 36\times \frac{x-4}{x+6} kot enojni ulomek.

$$\frac{4,5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Pomnožite 18x-54 s/z \frac{x+6}{x+6}.

$$\frac{4,5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{\left(18x-54\right)\left(x+6\right)}{x+6} in \frac{-3\left(x-4\right)x^{2}}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4,5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{30x^{2}+54x-324-3x^{3}}{x+6} in \frac{-12\left(x-4\right)x}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4,5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

\frac{18x^{2}+102x-324-3x^{3}}{x+6} in \frac{36\left(x-4\right)}{x+6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Izvedi množenje v 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4,5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Združite podobne člene v 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4,5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4,5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Okrajšaj x+6 v števcu in imenovalcu.

$$\frac{4,5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Razširite izraz.

$$\frac{4,5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Združite 4,5x^{2} in -3x^{2}, da dobite 1,5x^{2}.

$$\frac{1,5x^{2}+36x-78}{x^{2}+29x+78}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Okrajšaj x+26 v števcu in imenovalcu.

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

Razširite izraz.

$$\frac{\frac{3}{2}x-3}{x+3}$$