Lahenda x-1/x^2+4x+3+2/x^2+5x+6

$$\frac { x - 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 2 } { x ^ { 2 } + 5 x + 6 }$$

Arvuta

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Lühike lahenduskäik

Tegurda x^{2}+4x+3. Tegurda x^{2}+5x+6.

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

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

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

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

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

Tehke korrutustehted võrrandis \left(x-1\right)\left(x+2\right)+2\left(x+1\right).

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

Kombineerige sarnased liikmed avaldises x^{2}+2x-x-2+2x+2.

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

Kui avaldised pole tehtes \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} veel teguriteks lahutatud, tehke seda.

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

Taandage x+3 nii lugejas kui ka nimetajas.

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Laiendage \left(x+1\right)\left(x+2\right).

$$\frac{x}{x^{2}+3x+2}$$

Laienda

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Lühike lahenduskäik

Tegurda x^{2}+4x+3. Tegurda x^{2}+5x+6.

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

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

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

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

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

Tehke korrutustehted võrrandis \left(x-1\right)\left(x+2\right)+2\left(x+1\right).

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

Kombineerige sarnased liikmed avaldises x^{2}+2x-x-2+2x+2.

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

Kui avaldised pole tehtes \frac{x^{2}+3x}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} veel teguriteks lahutatud, tehke seda.

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

Taandage x+3 nii lugejas kui ka nimetajas.

$$\frac{x}{\left(x+1\right)\left(x+2\right)}$$

Laiendage \left(x+1\right)\left(x+2\right).

$$\frac{x}{x^{2}+3x+2}$$