Riješi x+4/x+3-x-3/x+4/14=

$$\frac { \frac { x + 4 } { x + 3 } - \frac { x - 3 } { x + 4 } } { 14 } =$$

Izračunaj

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

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}.

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

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.

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

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

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

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

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

Izrazite \frac{\frac{8x+25}{\left(x+3\right)\left(x+4\right)}}{14} kao jedan razlomak.

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x+3 sa svakim dijelom izraza x+4.

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

Kombinirajte 4x i 3x da biste dobili 7x.

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

Koristite svojstvo distributivnosti da biste pomnožili x^{2}+7x+12 s 14.

$$\frac{8x+25}{14x^{2}+98x+168}$$

Proširi

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

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}.

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

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.

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

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

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

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

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

Izrazite \frac{\frac{8x+25}{\left(x+3\right)\left(x+4\right)}}{14} kao jedan razlomak.

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x+3 sa svakim dijelom izraza x+4.

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

Kombinirajte 4x i 3x da biste dobili 7x.

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

Koristite svojstvo distributivnosti da biste pomnožili x^{2}+7x+12 s 14.

$$\frac{8x+25}{14x^{2}+98x+168}$$