Rešite 1/3+1/2n+1-1/2n+3

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

Ovrednoti

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 3 in 2n+1 je 3\left(2n+1\right). Pomnožite \frac{1}{3} s/z \frac{2n+1}{2n+1}. Pomnožite \frac{1}{2n+1} s/z \frac{3}{3}.

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

\frac{2n+1}{3\left(2n+1\right)} in \frac{3}{3\left(2n+1\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Združite podobne člene v 2n+1+3.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 3\left(2n+1\right) in 2n+3 je 3\left(2n+1\right)\left(2n+3\right). Pomnožite \frac{2n+4}{3\left(2n+1\right)} s/z \frac{2n+3}{2n+3}. Pomnožite \frac{1}{2n+3} s/z \frac{3\left(2n+1\right)}{3\left(2n+1\right)}.

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

Ker \frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)} in \frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v \left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right).

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

Združite podobne člene v 4n^{2}+6n+8n+12-6n-3.

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

Razčlenite 3\left(2n+1\right)\left(2n+3\right).

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

Faktoriziraj

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