Riješi x^2+x/x^2-49+x^2-1/x^2+17x+70

$$\frac { x ^ { 2 } + x } { x ^ { 2 } - 49 } + \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 17 x + 70 }$$

Izračunaj

$$\frac{\left(x+1\right)\left(2x^{2}+2x+7\right)}{\left(x+10\right)\left(x^{2}-49\right)}$$

Kratki koraci za rješenje

Rastavite x^{2}-49 na faktore. Rastavite x^{2}+17x+70 na faktore.

$$\frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)}+\frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-7\right)\left(x+7\right) i \left(x+7\right)\left(x+10\right) jest \left(x-7\right)\left(x+7\right)\left(x+10\right). Pomnožite \frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)} i \frac{x+10}{x+10}. Pomnožite \frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)} i \frac{x-7}{x-7}.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}+\frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Budući da \frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} i \frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Pomnožite izraz \left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right).

$$\frac{x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kombinirajte slične izraze u x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7.

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Proširivanje broja \left(x-7\right)\left(x+7\right)\left(x+10\right).

$$\frac{2x^{3}+4x^{2}+9x+7}{x^{3}+10x^{2}-49x-490}$$

Proširi

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x+10\right)\left(x^{2}-49\right)}$$

Kratki koraci za rješenje

Rastavite x^{2}-49 na faktore. Rastavite x^{2}+17x+70 na faktore.

$$\frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)}+\frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x-7\right)\left(x+7\right) i \left(x+7\right)\left(x+10\right) jest \left(x-7\right)\left(x+7\right)\left(x+10\right). Pomnožite \frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)} i \frac{x+10}{x+10}. Pomnožite \frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)} i \frac{x-7}{x-7}.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}+\frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Budući da \frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} i \frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Pomnožite izraz \left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right).

$$\frac{x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kombinirajte slične izraze u x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7.

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Proširivanje broja \left(x-7\right)\left(x+7\right)\left(x+10\right).

$$\frac{2x^{3}+4x^{2}+9x+7}{x^{3}+10x^{2}-49x-490}$$