Rešite 1/(2n-1)^2+1/4n^2

$$\frac { 1 } { ( 2 n - 1 ) ^ { 2 } } + \frac { 1 } { 4 n ^ { 2 } }$$

Ovrednoti

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

Kratka navodila za rešitev

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

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

\frac{4n^{2}}{4n^{2}\left(2n-1\right)^{2}} in \frac{\left(2n-1\right)^{2}}{4n^{2}\left(2n-1\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v 4n^{2}+\left(2n-1\right)^{2}.

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

Združite podobne člene v 4n^{2}+4n^{2}-4n+1.

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

Razčlenite 4n^{2}\left(2n-1\right)^{2}.

$$\frac{8n^{2}-4n+1}{16n^{4}-16n^{3}+4n^{2}}$$

Razširi

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

Kratka navodila za rešitev

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

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

\frac{4n^{2}}{4n^{2}\left(2n-1\right)^{2}} in \frac{\left(2n-1\right)^{2}}{4n^{2}\left(2n-1\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v 4n^{2}+\left(2n-1\right)^{2}.

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

Združite podobne člene v 4n^{2}+4n^{2}-4n+1.

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

Razčlenite 4n^{2}\left(2n-1\right)^{2}.

$$\frac{8n^{2}-4n+1}{16n^{4}-16n^{3}+4n^{2}}$$