Riješi x+4/x+3-x-3/x+4/frac{14{x^2+7x+12}}

$$\frac{ \frac{ x+4 }{ x+3 } - \frac{ x-3 }{ x+4 } }{ \frac{ 14 }{ { x }^{ 2 } +7x+12 } }$$

Izračunaj

$$\frac{4x}{7}+\frac{25}{14}$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+3 i x+4 jest \left(x+3\right)\left(x+4\right). Pomnožite \frac{x+4}{x+3} i \frac{x+4}{x+4}. Pomnožite \frac{x-3}{x+4} i \frac{x+3}{x+3}.

$$\frac{\frac{\left(x+4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)}-\frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Budući da \frac{\left(x+4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)} i \frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\frac{\left(x+4\right)\left(x+4\right)-\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Pomnožite izraz \left(x+4\right)\left(x+4\right)-\left(x-3\right)\left(x+3\right).

$$\frac{\frac{x^{2}+4x+4x+16-x^{2}-3x+3x+9}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Kombinirajte slične izraze u x^{2}+4x+4x+16-x^{2}-3x+3x+9.

$$\frac{\frac{8x+25}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Podijelite \frac{8x+25}{\left(x+3\right)\left(x+4\right)} s \frac{14}{x^{2}+7x+12} tako da pomnožite \frac{8x+25}{\left(x+3\right)\left(x+4\right)} s brojem recipročnim broju \frac{14}{x^{2}+7x+12}.

$$\frac{\left(8x+25\right)\left(x^{2}+7x+12\right)}{\left(x+3\right)\left(x+4\right)\times 14}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{\left(x+3\right)\left(x+4\right)\left(8x+25\right)}{14\left(x+3\right)\left(x+4\right)}$$

Skratite \left(x+3\right)\left(x+4\right) u brojniku i nazivniku.

$$\frac{8x+25}{14}$$

Proširi

$$\frac{4x}{7}+\frac{25}{14}$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+3 i x+4 jest \left(x+3\right)\left(x+4\right). Pomnožite \frac{x+4}{x+3} i \frac{x+4}{x+4}. Pomnožite \frac{x-3}{x+4} i \frac{x+3}{x+3}.

$$\frac{\frac{\left(x+4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)}-\frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Budući da \frac{\left(x+4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)} i \frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\frac{\left(x+4\right)\left(x+4\right)-\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Pomnožite izraz \left(x+4\right)\left(x+4\right)-\left(x-3\right)\left(x+3\right).

$$\frac{\frac{x^{2}+4x+4x+16-x^{2}-3x+3x+9}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Kombinirajte slične izraze u x^{2}+4x+4x+16-x^{2}-3x+3x+9.

$$\frac{\frac{8x+25}{\left(x+3\right)\left(x+4\right)}}{\frac{14}{x^{2}+7x+12}}$$

Podijelite \frac{8x+25}{\left(x+3\right)\left(x+4\right)} s \frac{14}{x^{2}+7x+12} tako da pomnožite \frac{8x+25}{\left(x+3\right)\left(x+4\right)} s brojem recipročnim broju \frac{14}{x^{2}+7x+12}.

$$\frac{\left(8x+25\right)\left(x^{2}+7x+12\right)}{\left(x+3\right)\left(x+4\right)\times 14}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{\left(x+3\right)\left(x+4\right)\left(8x+25\right)}{14\left(x+3\right)\left(x+4\right)}$$

Skratite \left(x+3\right)\left(x+4\right) u brojniku i nazivniku.

$$\frac{8x+25}{14}$$