Lahenda b^2+2/b^4-1+3/1-b^4

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

Arvuta

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

Lühike lahenduskäik

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

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right) ja \left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right) vähim ühiskordne on \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right). Korrutage omavahel \frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)} ja \frac{-1}{-1}.

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

Kuna murdudel \frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} ja \frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis b^{2}+2+3\left(-1\right).

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

Kombineerige sarnased liikmed avaldises b^{2}+2-3.

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

Kui avaldised pole tehtes \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} veel teguriteks lahutatud, tehke seda.

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

Taandage \left(b-1\right)\left(b+1\right) nii lugejas kui ka nimetajas.

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

Laienda

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

Lühike lahenduskäik

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

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right) ja \left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right) vähim ühiskordne on \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right). Korrutage omavahel \frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)} ja \frac{-1}{-1}.

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

Kuna murdudel \frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} ja \frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis b^{2}+2+3\left(-1\right).

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

Kombineerige sarnased liikmed avaldises b^{2}+2-3.

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

Kui avaldised pole tehtes \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} veel teguriteks lahutatud, tehke seda.

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

Taandage \left(b-1\right)\left(b+1\right) nii lugejas kui ka nimetajas.

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