frac{x^{2}-x-2}{x^{2}-9}div(x^2-2x-3/3x^2-7x-6*3x^2-10x-8/x^2+x-12) eching

$$\frac { x ^ { 2 } - x - 2 } { x ^ { 2 } - 9 } \div ( \frac { x ^ { 2 } - 2 x - 3 } { 3 x ^ { 2 } - 7 x - 6 } \times \frac { 3 x ^ { 2 } - 10 x - 8 } { x ^ { 2 } + x - 12 } )$$

Baholash

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

Qisqa yechim qadamlari

\frac{x^{2}-2x-3}{3x^{2}-7x-6} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(3x+2\right)}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Surat va maxrajdagi ikkala x-3 ni qisqartiring.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{x+1}{3x+2}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x+1}{3x+2} ni \frac{3x^{2}-10x-8}{x^{2}+x-12} ga ko‘paytiring.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}}$$

\frac{x^{2}-x-2}{x^{2}-9} ni \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} ga bo'lish \frac{x^{2}-x-2}{x^{2}-9} ga k'paytirish \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} ga qaytarish.

$$\frac{\left(x^{2}-x-2\right)\left(3x+2\right)\left(x^{2}+x-12\right)}{\left(x^{2}-9\right)\left(x+1\right)\left(3x^{2}-10x-8\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala \left(x-3\right)\left(x+1\right)\left(3x+2\right) ni qisqartiring.

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

Ifodani kengaytiring.

$$\frac{x^{2}+2x-8}{x^{2}-x-12}$$

Kengaytirish

$$\frac{x^{2}+2x-8}{\left(x-4\right)\left(x+3\right)}$$

Qisqa yechim qadamlari

\frac{x^{2}-2x-3}{3x^{2}-7x-6} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(3x+2\right)}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Surat va maxrajdagi ikkala x-3 ni qisqartiring.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{x+1}{3x+2}\times \frac{3x^{2}-10x-8}{x^{2}+x-12}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x+1}{3x+2} ni \frac{3x^{2}-10x-8}{x^{2}+x-12} ga ko‘paytiring.

$$\frac{\frac{x^{2}-x-2}{x^{2}-9}}{\frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)}}$$

\frac{x^{2}-x-2}{x^{2}-9} ni \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} ga bo'lish \frac{x^{2}-x-2}{x^{2}-9} ga k'paytirish \frac{\left(x+1\right)\left(3x^{2}-10x-8\right)}{\left(3x+2\right)\left(x^{2}+x-12\right)} ga qaytarish.

$$\frac{\left(x^{2}-x-2\right)\left(3x+2\right)\left(x^{2}+x-12\right)}{\left(x^{2}-9\right)\left(x+1\right)\left(3x^{2}-10x-8\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala \left(x-3\right)\left(x+1\right)\left(3x+2\right) ni qisqartiring.

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

Ifodani kengaytiring.

$$\frac{x^{2}+2x-8}{x^{2}-x-12}$$