Issolvi 3/2x+1-1/3x+2=2g

$$\frac { 3 } { 2 x + 1 } - \frac { 1 } { 3 x + 2 } = 2 g$$

Solvi għal g

$$g=\frac{7x+5}{2\left(6x^{2}+7x+2\right)}$$

$$x\neq -\frac{1}{2}\text{ and }x\neq -\frac{2}{3}$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(2x+1\right)\left(3x+2\right), l-inqas denominatur komuni ta' 2x+1,3x+2.

$$\left(3x+2\right)\times 3-\left(2x+1\right)=2g\left(2x+1\right)\left(3x+2\right)$$

Uża l-propjetà distributtiva biex timmultiplika 3x+2 b'3.

$$9x+6-\left(2x+1\right)=2g\left(2x+1\right)\left(3x+2\right)$$

Biex issib l-oppost ta' 2x+1, sib l-oppost ta' kull terminu.

$$9x+6-2x-1=2g\left(2x+1\right)\left(3x+2\right)$$

Ikkombina 9x u -2x biex tikseb 7x.

$$7x+6-1=2g\left(2x+1\right)\left(3x+2\right)$$

Naqqas 1 minn 6 biex tikseb 5.

$$7x+5=2g\left(2x+1\right)\left(3x+2\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2g b'2x+1.

$$7x+5=\left(4xg+2g\right)\left(3x+2\right)$$

Uża l-propjetà distributtiva biex timmultiplika 4xg+2g b'3x+2 u kkombina termini simili.

$$7x+5=12gx^{2}+14gx+4g$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$12gx^{2}+14gx+4g=7x+5$$

Ikkombina t-termini kollha li fihom g.

$$\left(12x^{2}+14x+4\right)g=7x+5$$

Iddividi ż-żewġ naħat b'12x^{2}+14x+4.

$$\frac{\left(12x^{2}+14x+4\right)g}{12x^{2}+14x+4}=\frac{7x+5}{12x^{2}+14x+4}$$

Meta tiddividi b'12x^{2}+14x+4 titneħħa l-multiplikazzjoni b'12x^{2}+14x+4.

$$g=\frac{7x+5}{12x^{2}+14x+4}$$

Iddividi 7x+5 b'12x^{2}+14x+4.

$$g=\frac{7x+5}{2\left(6x^{2}+7x+2\right)}$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{; }x=-\frac{-\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{, }&g\neq 0\\x=-\frac{5}{7}\text{, }&g=0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=-\frac{\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{; }x=-\frac{-\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{, }&g\leq -3\sqrt{2}-\frac{11}{2}\text{ or }\left(g\neq 0\text{ and }g\geq 3\sqrt{2}-\frac{11}{2}\right)\\x=-\frac{5}{7}\text{, }&g=0\end{matrix}\right.$$