Lahenda [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=

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

Arvuta

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

Lühike lahenduskäik

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel x^{4} ja \frac{x^{2}+1}{x^{2}+1}.

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

Kuna murdudel \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} ja \frac{x^{4}+1}{x^{2}+1} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

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

Kombineerige sarnased liikmed avaldises x^{6}+x^{4}-x^{4}-1.

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

Korrutage omavahel \frac{x^{6}-1}{x^{2}+1} ja \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Taandage x^{2}+1 nii lugejas kui ka nimetajas.

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

Kui avaldised pole tehtes \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6} veel teguriteks lahutatud, tehke seda.

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

Taandage \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) nii lugejas kui ka nimetajas.

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

Jagage 1,5-\frac{x-4}{x+6} väärtusega \frac{x^{2}+29x+78}{3x^{2}+12x-36}, korrutades 1,5-\frac{x-4}{x+6} väärtuse \frac{x^{2}+29x+78}{3x^{2}+12x-36} pöördväärtusega.

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

Kasutage distributiivsusomadust, et korrutada 1,5-\frac{x-4}{x+6} ja 3x^{2}+12x-36.

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

Avaldage -3\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldage \frac{-3\left(x-4\right)}{x+6}x^{2} ühe murdarvuna.

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

Avaldage -12\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldage \frac{-12\left(x-4\right)}{x+6}x ühe murdarvuna.

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

Avaldage 36\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 18x-54 ja \frac{x+6}{x+6}.

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

Kuna murdudel \frac{\left(18x-54\right)\left(x+6\right)}{x+6} ja \frac{-3\left(x-4\right)x^{2}}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

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

Kombineerige sarnased liikmed avaldises 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

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

Kuna murdudel \frac{30x^{2}+54x-324-3x^{3}}{x+6} ja \frac{-12\left(x-4\right)x}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

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

Kombineerige sarnased liikmed avaldises 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

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

Kuna murdudel \frac{18x^{2}+102x-324-3x^{3}}{x+6} ja \frac{36\left(x-4\right)}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

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

Kombineerige sarnased liikmed avaldises 18x^{2}+102x-324-3x^{3}+36x-144.

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

Kui avaldised pole tehtes \frac{18x^{2}+138x-468-3x^{3}}{x+6} veel teguriteks lahutatud, tehke seda.

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

Taandage x+6 nii lugejas kui ka nimetajas.

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

Laiendage avaldist.

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

Kombineerige 4,5x^{2} ja -3x^{2}, et leida 1,5x^{2}.

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

Kui avaldised pole juba teguriteks lahutatud, tehke seda.

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

Taandage x+26 nii lugejas kui ka nimetajas.

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

Laiendage avaldist.

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

Laienda

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

Lühike lahenduskäik

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel x^{4} ja \frac{x^{2}+1}{x^{2}+1}.

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

Kuna murdudel \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} ja \frac{x^{4}+1}{x^{2}+1} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

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

Kombineerige sarnased liikmed avaldises x^{6}+x^{4}-x^{4}-1.

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

Korrutage omavahel \frac{x^{6}-1}{x^{2}+1} ja \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Taandage x^{2}+1 nii lugejas kui ka nimetajas.

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

Kui avaldised pole tehtes \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6} veel teguriteks lahutatud, tehke seda.

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

Taandage \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) nii lugejas kui ka nimetajas.

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

Jagage 1,5-\frac{x-4}{x+6} väärtusega \frac{x^{2}+29x+78}{3x^{2}+12x-36}, korrutades 1,5-\frac{x-4}{x+6} väärtuse \frac{x^{2}+29x+78}{3x^{2}+12x-36} pöördväärtusega.

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

Kasutage distributiivsusomadust, et korrutada 1,5-\frac{x-4}{x+6} ja 3x^{2}+12x-36.

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

Avaldage -3\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldage \frac{-3\left(x-4\right)}{x+6}x^{2} ühe murdarvuna.

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

Avaldage -12\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldage \frac{-12\left(x-4\right)}{x+6}x ühe murdarvuna.

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

Avaldage 36\times \frac{x-4}{x+6} ühe murdarvuna.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 18x-54 ja \frac{x+6}{x+6}.

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

Kuna murdudel \frac{\left(18x-54\right)\left(x+6\right)}{x+6} ja \frac{-3\left(x-4\right)x^{2}}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

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

Kombineerige sarnased liikmed avaldises 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

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

Kuna murdudel \frac{30x^{2}+54x-324-3x^{3}}{x+6} ja \frac{-12\left(x-4\right)x}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

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

Kombineerige sarnased liikmed avaldises 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

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

Kuna murdudel \frac{18x^{2}+102x-324-3x^{3}}{x+6} ja \frac{36\left(x-4\right)}{x+6} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

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

Kombineerige sarnased liikmed avaldises 18x^{2}+102x-324-3x^{3}+36x-144.

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

Kui avaldised pole tehtes \frac{18x^{2}+138x-468-3x^{3}}{x+6} veel teguriteks lahutatud, tehke seda.

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

Taandage x+6 nii lugejas kui ka nimetajas.

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

Laiendage avaldist.

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

Kombineerige 4,5x^{2} ja -3x^{2}, et leida 1,5x^{2}.

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

Kui avaldised pole juba teguriteks lahutatud, tehke seda.

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

Taandage x+26 nii lugejas kui ka nimetajas.

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

Laiendage avaldist.

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