Issolvi 3x+5/6x^{2+3x}+4x^2+9/4x^2-1=x+3/2/3x-frac{8}{3}frac{x^2}{(1-4x^2)}

$$\frac { 3 x + 5 } { 6 x ^ { 2 } + 3 x } + \frac { 4 x ^ { 2 } + 9 } { 4 x ^ { 2 } - 1 } = \frac { x + \frac { 3 } { 2 } } { 3 x } - \frac { 8 } { 3 } \frac { x ^ { 2 } } { ( 1 - 4 x ^ { 2 } ) }$$

Solvi għal x

$$x=\frac{1}{10}=0.1$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -\frac{1}{2},0,\frac{1}{2} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'3x\left(2x-1\right)\left(2x+1\right), l-inqas denominatur komuni ta' 6x^{2}+3x,4x^{2}-1,3x,3,1-4x^{2}.

$$\left(2x-1\right)\left(3x+5\right)+3x\left(4x^{2}+9\right)=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 2x-1 b'3x+5 u kkombina termini simili.

$$6x^{2}+7x-5+3x\left(4x^{2}+9\right)=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 3x b'4x^{2}+9.

$$6x^{2}+7x-5+12x^{3}+27x=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

Ikkombina 7x u 27x biex tikseb 34x.

$$6x^{2}+34x-5+12x^{3}=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)xx^{2}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 1 u 2 biex tikseb 3.

$$6x^{2}+34x-5+12x^{3}=\left(4x^{2}-1\right)\left(x+\frac{3}{2}\right)-\frac{8}{3}\left(-3\right)x^{3}$$

Uża l-propjetà distributtiva biex timmultiplika 4x^{2}-1 b'x+\frac{3}{2}.

$$6x^{2}+34x-5+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}-\frac{8}{3}\left(-3\right)x^{3}$$

Immultiplika \frac{8}{3} u -3 biex tikseb -8.

$$6x^{2}+34x-5+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}-\left(-8x^{3}\right)$$

L-oppost ta' -8x^{3} huwa 8x^{3}.

$$6x^{2}+34x-5+12x^{3}=4x^{3}+6x^{2}-x-\frac{3}{2}+8x^{3}$$

Ikkombina 4x^{3} u 8x^{3} biex tikseb 12x^{3}.

$$6x^{2}+34x-5+12x^{3}=12x^{3}+6x^{2}-x-\frac{3}{2}$$

Naqqas 12x^{3} miż-żewġ naħat.

$$6x^{2}+34x-5+12x^{3}-12x^{3}=6x^{2}-x-\frac{3}{2}$$

Ikkombina 12x^{3} u -12x^{3} biex tikseb 0.

$$6x^{2}+34x-5=6x^{2}-x-\frac{3}{2}$$

Naqqas 6x^{2} miż-żewġ naħat.

$$6x^{2}+34x-5-6x^{2}=-x-\frac{3}{2}$$

Ikkombina 6x^{2} u -6x^{2} biex tikseb 0.

$$34x-5=-x-\frac{3}{2}$$

Żid x maż-żewġ naħat.

$$34x-5+x=-\frac{3}{2}$$

Ikkombina 34x u x biex tikseb 35x.

$$35x-5=-\frac{3}{2}$$

Żid 5 maż-żewġ naħat.

$$35x=-\frac{3}{2}+5$$

Żid -\frac{3}{2} u 5 biex tikseb \frac{7}{2}.

$$35x=\frac{7}{2}$$

Iddividi ż-żewġ naħat b'35.

$$x=\frac{\frac{7}{2}}{35}$$

Esprimi \frac{\frac{7}{2}}{35} bħala frazzjoni waħda.

$$x=\frac{7}{2\times 35}$$

Immultiplika 2 u 35 biex tikseb 70.

$$x=\frac{7}{70}$$

Naqqas il-frazzjoni \frac{7}{70} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 7.

$$x=\frac{1}{10}$$