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

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

g uchun yechish

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

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini \left(2x+1\right)\left(3x+2\right) ga, 2x+1,3x+2 ning eng kichik karralisiga ko‘paytiring.

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

3x+2 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

2x+1 teskarisini topish uchun har birining teskarisini toping.

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

7x ni olish uchun 9x va -2x ni birlashtirish.

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

5 olish uchun 6 dan 1 ni ayirish.

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

2g ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

4xg+2g ga 3x+2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

g'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini 12x^{2}+14x+4 ga bo‘ling.

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

12x^{2}+14x+4 ga bo'lish 12x^{2}+14x+4 ga ko'paytirishni bekor qiladi.

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

7x+5 ni 12x^{2}+14x+4 ga bo'lish.

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

x uchun yechish (complex solution)

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

x uchun yechish

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