Lahenda x^2+x/x^2-49+x^2-1/x^2+17x+70

$$\frac { x ^ { 2 } + x } { x ^ { 2 } - 49 } + \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 17 x + 70 }$$

Arvuta

$$\frac{\left(x+1\right)\left(2x^{2}+2x+7\right)}{\left(x+10\right)\left(x^{2}-49\right)}$$

Lühike lahenduskäik

Tegurda x^{2}-49. Tegurda x^{2}+17x+70.

$$\frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)}+\frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x-7\right)\left(x+7\right) ja \left(x+7\right)\left(x+10\right) vähim ühiskordne on \left(x-7\right)\left(x+7\right)\left(x+10\right). Korrutage omavahel \frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)} ja \frac{x+10}{x+10}. Korrutage omavahel \frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)} ja \frac{x-7}{x-7}.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}+\frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kuna murdudel \frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} ja \frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Tehke korrutustehted võrrandis \left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right).

$$\frac{x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kombineerige sarnased liikmed avaldises x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7.

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Laiendage \left(x-7\right)\left(x+7\right)\left(x+10\right).

$$\frac{2x^{3}+4x^{2}+9x+7}{x^{3}+10x^{2}-49x-490}$$

Laienda

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x+10\right)\left(x^{2}-49\right)}$$

Lühike lahenduskäik

Tegurda x^{2}-49. Tegurda x^{2}+17x+70.

$$\frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)}+\frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x-7\right)\left(x+7\right) ja \left(x+7\right)\left(x+10\right) vähim ühiskordne on \left(x-7\right)\left(x+7\right)\left(x+10\right). Korrutage omavahel \frac{x^{2}+x}{\left(x-7\right)\left(x+7\right)} ja \frac{x+10}{x+10}. Korrutage omavahel \frac{x^{2}-1}{\left(x+7\right)\left(x+10\right)} ja \frac{x-7}{x-7}.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}+\frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kuna murdudel \frac{\left(x^{2}+x\right)\left(x+10\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} ja \frac{\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{\left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right)}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Tehke korrutustehted võrrandis \left(x^{2}+x\right)\left(x+10\right)+\left(x^{2}-1\right)\left(x-7\right).

$$\frac{x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Kombineerige sarnased liikmed avaldises x^{3}+10x^{2}+x^{2}+10x+x^{3}-7x^{2}-x+7.

$$\frac{2x^{3}+4x^{2}+9x+7}{\left(x-7\right)\left(x+7\right)\left(x+10\right)}$$

Laiendage \left(x-7\right)\left(x+7\right)\left(x+10\right).

$$\frac{2x^{3}+4x^{2}+9x+7}{x^{3}+10x^{2}-49x-490}$$