다음을 풀어보세요: (x^2-x-2)(x^2-x-5)+2/(x^2-x-1)(x^2-x-5)+4

$$\frac { ( x ^ { 2 } - x - 2 ) ( x ^ { 2 } - x - 5 ) + 2 } { ( x ^ { 2 } - x - 1 ) ( x ^ { 2 } - x - 5 ) + 4 }$$

계산

$$-\frac{x^{2}-x-4}{3+x-x^{2}}$$

간단한 해답 단계

인수 분해되지 않은 식을 인수 분해합니다.

$$\frac{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(-\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)^{2}\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)^{2}}$$

분자와 분모 모두에서 \left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)을(를) 상쇄합니다.

$$\frac{\left(x-\left(-\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)}$$

식을 확장합니다.

$$\frac{x^{2}-x-4}{x^{2}-x-3}$$

확장

$$\frac{x^{2}-x-4}{x^{2}-x-3}$$

간단한 해답 단계

인수 분해되지 않은 식을 인수 분해합니다.

$$\frac{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(-\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)^{2}\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)^{2}}$$

분자와 분모 모두에서 \left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)을(를) 상쇄합니다.

$$\frac{\left(x-\left(-\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}+\frac{1}{2}\right)\right)}{\left(x-\left(-\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{13}+\frac{1}{2}\right)\right)}$$

식을 확장합니다.

$$\frac{x^{2}-x-4}{x^{2}-x-3}$$