Riješi 1/3+1/2n+1-1/2n+3

$$\frac { 1 } { 3 } + \frac { 1 } { 2 n + 1 } - \frac { 1 } { 2 n + 3 }$$

Izračunaj

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva 3 i 2n+1 jest 3\left(2n+1\right). Pomnožite \frac{1}{3} i \frac{2n+1}{2n+1}. Pomnožite \frac{1}{2n+1} i \frac{3}{3}.

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

Budući da \frac{2n+1}{3\left(2n+1\right)} i \frac{3}{3\left(2n+1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Kombinirajte slične izraze u 2n+1+3.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva 3\left(2n+1\right) i 2n+3 jest 3\left(2n+1\right)\left(2n+3\right). Pomnožite \frac{2n+4}{3\left(2n+1\right)} i \frac{2n+3}{2n+3}. Pomnožite \frac{1}{2n+3} i \frac{3\left(2n+1\right)}{3\left(2n+1\right)}.

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

Budući da \frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)} i \frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right).

$$\frac{4n^{2}+6n+8n+12-6n-3}{3\left(2n+1\right)\left(2n+3\right)}$$

Kombinirajte slične izraze u 4n^{2}+6n+8n+12-6n-3.

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

Proširivanje broja 3\left(2n+1\right)\left(2n+3\right).

$$\frac{4n^{2}+8n+9}{12n^{2}+24n+9}$$

Faktor

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$