(x+3)(x+4)/(x+1)(x-1)*x^2(1+x)/x+4*x-1/3(x+3) eching

$$\frac { ( x + 3 ) ( x + 4 ) } { ( x + 1 ) ( x - 1 ) } \cdot \frac { x ^ { 2 } ( 1 + x ) } { x + 4 } \cdot \frac { x - 1 } { 3 ( x + 3 ) }$$

Baholash

$$\frac{x^{2}}{3}$$

Qisqa yechim qadamlari

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

$$\frac{x^{2}+7x+12}{\left(x+1\right)\left(x-1\right)}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Hisoblang: \left(x+1\right)\left(x-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

x^{2} ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

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

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3x+9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}+7x+12}{x^{2}-1} ni \frac{x^{2}+x^{3}}{x+4} ga ko‘paytiring.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)}\times \frac{x-1}{3x+9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)} ni \frac{x-1}{3x+9} ga ko‘paytiring.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)\left(x-1\right)}{\left(x^{2}-1\right)\left(x+4\right)\left(3x+9\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala \left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+4\right) ni qisqartiring.

$$\frac{x^{2}}{3}$$

Kengaytirish

$$\frac{x^{2}}{3}$$

Qisqa yechim qadamlari

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

$$\frac{x^{2}+7x+12}{\left(x+1\right)\left(x-1\right)}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Hisoblang: \left(x+1\right)\left(x-1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

x^{2} ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

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

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3x+9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}+7x+12}{x^{2}-1} ni \frac{x^{2}+x^{3}}{x+4} ga ko‘paytiring.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)}\times \frac{x-1}{3x+9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)} ni \frac{x-1}{3x+9} ga ko‘paytiring.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)\left(x-1\right)}{\left(x^{2}-1\right)\left(x+4\right)\left(3x+9\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala \left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+4\right) ni qisqartiring.

$$\frac{x^{2}}{3}$$