Lahenda 2x-1/16-x^2*x^2+3x-4/2x^2-3x+1=1/4-x

$$\frac { 2 x - 1 } { 16 - x ^ { 2 } } \cdot \frac { x ^ { 2 } + 3 x - 4 } { 2 x ^ { 2 } - 3 x + 1 } = \frac { 1 } { 4 - x }$$

Lahendage ja leidke x (complex solution)

$$x\in \mathrm{C}\setminus 4,-4,\frac{1}{2},1$$

Lühike lahenduskäik

Muutuja x ei tohi võrduda ühegagi väärtustest -4,\frac{1}{2},1,4, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled arvuga \left(x-4\right)\left(x-1\right)\left(2x-1\right)\left(x+4\right), mis on arvu 16-x^{2},2x^{2}-3x+1,4-x vähim ühiskordne.

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

Avaldage \left(-1+3x-2x^{2}\right)\times \frac{x^{2}+3x-4}{2x^{2}-3x+1} ühe murdarvuna.

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

Kasutage distributiivsusomadust, et korrutada \frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1} ja 2x-1.

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

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja x^{2}+3x-4, ning koondage sarnased liikmed.

$$2\times \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1}x-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Avaldage 2\times \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1} ühe murdarvuna.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}x-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Avaldage \frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}x ühe murdarvuna.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1}-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja x^{2}+3x-4, ning koondage sarnased liikmed.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1}-\frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kuna murdudel \frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1} ja \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1} on sama nimetaja, lahutage nende lugejad.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x-\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Tehke korrutustehted võrrandis 2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x-\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right).

$$\frac{32x^{3}-30x^{2}+8x-6x^{4}-4x^{5}-16x^{2}+15x-4+3x^{3}+2x^{4}}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kombineerige sarnased liikmed avaldises 32x^{3}-30x^{2}+8x-6x^{4}-4x^{5}-16x^{2}+15x-4+3x^{3}+2x^{4}.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1 ja -1+x.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=\left(1-x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada 1-x ja -1+2x, ning koondage sarnased liikmed.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=\left(-1+3x-2x^{2}\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja 4+x, ning koondage sarnased liikmed.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=-4+11x-5x^{2}-2x^{3}$$

Lahutage mõlemast poolest -4.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}-\left(-4\right)=11x-5x^{2}-2x^{3}$$

Arvu -4 vastand on 4.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}+4=11x-5x^{2}-2x^{3}$$

Tegurda 2x^{2}-3x+1.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)}+4=11x-5x^{2}-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 4 ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)}+\frac{4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Kuna murdudel \frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)} ja \frac{4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Tehke korrutustehted võrrandis 35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+4\left(x-1\right)\left(2x-1\right).

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+8x^{2}-4x-8x+4}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Kombineerige sarnased liikmed avaldises 35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+8x^{2}-4x-8x+4.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Lahutage mõlemast poolest 11x.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}-11x=-5x^{2}-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel -11x ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Kuna murdudel \frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Tehke korrutustehted võrrandis 35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-11x\left(x-1\right)\left(2x-1\right).

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-22x^{3}+11x^{2}+22x^{2}-11x}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Kombineerige sarnased liikmed avaldises 35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-22x^{3}+11x^{2}+22x^{2}-11x.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Liitke 5x^{2} mõlemale poolele.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+5x^{2}=-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 5x^{2} ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Kuna murdudel \frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}+5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Tehke korrutustehted võrrandis 13x^{3}-5x^{2}-4x^{4}-4x^{5}+5x^{2}\left(x-1\right)\left(2x-1\right).

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}+10x^{4}-5x^{3}-10x^{3}+5x^{2}}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Kombineerige sarnased liikmed avaldises 13x^{3}-5x^{2}-4x^{4}-4x^{5}+10x^{4}-5x^{3}-10x^{3}+5x^{2}.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Liitke 2x^{3} mõlemale poolele.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+2x^{3}=0$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 2x^{3} ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=0$$

Kuna murdudel \frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{-2x^{3}+6x^{4}-4x^{5}+2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=0$$

Tehke korrutustehted võrrandis -2x^{3}+6x^{4}-4x^{5}+2x^{3}\left(x-1\right)\left(2x-1\right).

$$\frac{-2x^{3}+6x^{4}-4x^{5}+4x^{5}-2x^{4}-4x^{4}+2x^{3}}{\left(x-1\right)\left(2x-1\right)}=0$$

Kombineerige sarnased liikmed avaldises -2x^{3}+6x^{4}-4x^{5}+4x^{5}-2x^{4}-4x^{4}+2x^{3}.

$$\frac{0}{\left(x-1\right)\left(2x-1\right)}=0$$

Muutuja x ei tohi võrduda ühegagi väärtustest \frac{1}{2},1, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled \left(x-1\right)\left(2x-1\right)-ga.

$$0=0$$

See kehtib iga muutuja x väärtuse korral.

$$x\in \mathrm{C}$$

Muutuja x ei tohi võrduda ühegagi väärtustest \frac{1}{2},1,-4,4.

$$x\in \mathrm{C}\setminus -4,\frac{1}{2},1,4$$

Lahendage ja leidke x

$$x\in \mathrm{R}\setminus 4,-4,1,\frac{1}{2}$$

Lühike lahenduskäik

Muutuja x ei tohi võrduda ühegagi väärtustest -4,\frac{1}{2},1,4, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled arvuga \left(x-4\right)\left(x-1\right)\left(2x-1\right)\left(x+4\right), mis on arvu 16-x^{2},2x^{2}-3x+1,4-x vähim ühiskordne.

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

Avaldage \left(-1+3x-2x^{2}\right)\times \frac{x^{2}+3x-4}{2x^{2}-3x+1} ühe murdarvuna.

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

Kasutage distributiivsusomadust, et korrutada \frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1} ja 2x-1.

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

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja x^{2}+3x-4, ning koondage sarnased liikmed.

$$2\times \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1}x-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Avaldage 2\times \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1} ühe murdarvuna.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}x-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Avaldage \frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}x ühe murdarvuna.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1}-\frac{\left(-1+3x-2x^{2}\right)\left(x^{2}+3x-4\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja x^{2}+3x-4, ning koondage sarnased liikmed.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1}-\frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kuna murdudel \frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x}{2x^{2}-3x+1} ja \frac{16x^{2}-15x+4-3x^{3}-2x^{4}}{2x^{2}-3x+1} on sama nimetaja, lahutage nende lugejad.

$$\frac{2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x-\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Tehke korrutustehted võrrandis 2\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right)x-\left(16x^{2}-15x+4-3x^{3}-2x^{4}\right).

$$\frac{32x^{3}-30x^{2}+8x-6x^{4}-4x^{5}-16x^{2}+15x-4+3x^{3}+2x^{4}}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kombineerige sarnased liikmed avaldises 32x^{3}-30x^{2}+8x-6x^{4}-4x^{5}-16x^{2}+15x-4+3x^{3}+2x^{4}.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=-\left(-1+x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1 ja -1+x.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=\left(1-x\right)\left(-1+2x\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada 1-x ja -1+2x, ning koondage sarnased liikmed.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=\left(-1+3x-2x^{2}\right)\left(4+x\right)$$

Kasutage distributiivsusomadust, et korrutada -1+3x-2x^{2} ja 4+x, ning koondage sarnased liikmed.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}=-4+11x-5x^{2}-2x^{3}$$

Lahutage mõlemast poolest -4.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}-\left(-4\right)=11x-5x^{2}-2x^{3}$$

Arvu -4 vastand on 4.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{2x^{2}-3x+1}+4=11x-5x^{2}-2x^{3}$$

Tegurda 2x^{2}-3x+1.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)}+4=11x-5x^{2}-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 4 ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)}+\frac{4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Kuna murdudel \frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4}{\left(x-1\right)\left(2x-1\right)} ja \frac{4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+4\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Tehke korrutustehted võrrandis 35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+4\left(x-1\right)\left(2x-1\right).

$$\frac{35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+8x^{2}-4x-8x+4}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Kombineerige sarnased liikmed avaldises 35x^{3}-46x^{2}+23x-4x^{4}-4x^{5}-4+8x^{2}-4x-8x+4.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=11x-5x^{2}-2x^{3}$$

Lahutage mõlemast poolest 11x.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}-11x=-5x^{2}-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel -11x ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Kuna murdudel \frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-11x\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Tehke korrutustehted võrrandis 35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-11x\left(x-1\right)\left(2x-1\right).

$$\frac{35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-22x^{3}+11x^{2}+22x^{2}-11x}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Kombineerige sarnased liikmed avaldises 35x^{3}-38x^{2}+11x-4x^{4}-4x^{5}-22x^{3}+11x^{2}+22x^{2}-11x.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=-5x^{2}-2x^{3}$$

Liitke 5x^{2} mõlemale poolele.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+5x^{2}=-2x^{3}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 5x^{2} ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Kuna murdudel \frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}+5x^{2}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Tehke korrutustehted võrrandis 13x^{3}-5x^{2}-4x^{4}-4x^{5}+5x^{2}\left(x-1\right)\left(2x-1\right).

$$\frac{13x^{3}-5x^{2}-4x^{4}-4x^{5}+10x^{4}-5x^{3}-10x^{3}+5x^{2}}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Kombineerige sarnased liikmed avaldises 13x^{3}-5x^{2}-4x^{4}-4x^{5}+10x^{4}-5x^{3}-10x^{3}+5x^{2}.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}=-2x^{3}$$

Liitke 2x^{3} mõlemale poolele.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+2x^{3}=0$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 2x^{3} ja \frac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}.

$$\frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)}+\frac{2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=0$$

Kuna murdudel \frac{-2x^{3}+6x^{4}-4x^{5}}{\left(x-1\right)\left(2x-1\right)} ja \frac{2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{-2x^{3}+6x^{4}-4x^{5}+2x^{3}\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(2x-1\right)}=0$$

Tehke korrutustehted võrrandis -2x^{3}+6x^{4}-4x^{5}+2x^{3}\left(x-1\right)\left(2x-1\right).

$$\frac{-2x^{3}+6x^{4}-4x^{5}+4x^{5}-2x^{4}-4x^{4}+2x^{3}}{\left(x-1\right)\left(2x-1\right)}=0$$

Kombineerige sarnased liikmed avaldises -2x^{3}+6x^{4}-4x^{5}+4x^{5}-2x^{4}-4x^{4}+2x^{3}.

$$\frac{0}{\left(x-1\right)\left(2x-1\right)}=0$$

Muutuja x ei tohi võrduda ühegagi väärtustest \frac{1}{2},1, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled \left(x-1\right)\left(2x-1\right)-ga.

$$0=0$$

See kehtib iga muutuja x väärtuse korral.

$$x\in \mathrm{R}$$

Muutuja x ei tohi võrduda ühegagi väärtustest \frac{1}{2},1,-4,4.

$$x\in \mathrm{R}\setminus -4,\frac{1}{2},1,4$$