Rešite b^2+2/b^4-1+3/1-b^4

$$\frac { b ^ { 2 } + 2 } { b ^ { 4 } - 1 } + \frac { 3 } { 1 - b ^ { 4 } }$$

Ovrednoti

$$\frac{1}{b^{2}+1}$$

Kratka navodila za rešitev

Faktorizirajte b^{4}-1. Faktorizirajte 1-b^{4}.

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

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

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

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

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

Izvedi množenje v b^{2}+2+3\left(-1\right).

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

Združite podobne člene v b^{2}+2-3.

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

Faktorizirajte izraze, ki še niso faktorizirani v \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}.

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

Okrajšaj \left(b-1\right)\left(b+1\right) v števcu in imenovalcu.

$$\frac{1}{b^{2}+1}$$

Razširi

$$\frac{1}{b^{2}+1}$$

Kratka navodila za rešitev

Faktorizirajte b^{4}-1. Faktorizirajte 1-b^{4}.

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

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

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

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

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

Izvedi množenje v b^{2}+2+3\left(-1\right).

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

Združite podobne člene v b^{2}+2-3.

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

Faktorizirajte izraze, ki še niso faktorizirani v \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}.

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

Okrajšaj \left(b-1\right)\left(b+1\right) v števcu in imenovalcu.

$$\frac{1}{b^{2}+1}$$