6x^2+13x-4/2x+5=12x^2+5x-2/4x+3 eching

$$\frac { 6 x ^ { 2 } + 13 x - 4 } { 2 x + 5 } = \frac { 12 x ^ { 2 } + 5 x - 2 } { 4 x + 3 }$$

x uchun yechish

$$x=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{5}{2},-\frac{3}{4} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(2x+5\right)\left(4x+3\right) ga, 2x+5,4x+3 ning eng kichik karralisiga ko‘paytiring.

$$\left(4x+3\right)\left(6x^{2}+13x-4\right)=\left(2x+5\right)\left(12x^{2}+5x-2\right)$$

4x+3 ga 6x^{2}+13x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$24x^{3}+70x^{2}+23x-12=\left(2x+5\right)\left(12x^{2}+5x-2\right)$$

2x+5 ga 12x^{2}+5x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$24x^{3}+70x^{2}+23x-12=24x^{3}+70x^{2}+21x-10$$

Ikkala tarafdan 24x^{3} ni ayirish.

$$24x^{3}+70x^{2}+23x-12-24x^{3}=70x^{2}+21x-10$$

0 ni olish uchun 24x^{3} va -24x^{3} ni birlashtirish.

$$70x^{2}+23x-12=70x^{2}+21x-10$$

Ikkala tarafdan 70x^{2} ni ayirish.

$$70x^{2}+23x-12-70x^{2}=21x-10$$

0 ni olish uchun 70x^{2} va -70x^{2} ni birlashtirish.

$$23x-12=21x-10$$

Ikkala tarafdan 21x ni ayirish.

$$23x-12-21x=-10$$

2x ni olish uchun 23x va -21x ni birlashtirish.

$$2x-12=-10$$

12 ni ikki tarafga qo’shing.

$$2x=-10+12$$

2 olish uchun -10 va 12'ni qo'shing.

$$2x=2$$

Ikki tarafini 2 ga bo‘ling.

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

1 ni olish uchun 2 ni 2 ga bo‘ling.

$$x=1$$