Lahenda x+1/x^2-9-x-1/x^2+6x+9

$$\frac{ x+1 }{ { x }^{ 2 } -9 } - \frac{ x-1 }{ { x }^{ 2 } +6x+9 }$$

Arvuta

$$\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}$$

Lühike lahenduskäik

Tegurda x^{2}-9. Tegurda x^{2}+6x+9.

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

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

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

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

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

Tehke korrutustehted võrrandis \left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right).

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

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

$$\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}$$

Laiendage \left(x-3\right)\left(x+3\right)^{2}.

$$\frac{8x}{x^{3}+3x^{2}-9x-27}$$

Laienda

$$\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}$$

Lühike lahenduskäik

Tegurda x^{2}-9. Tegurda x^{2}+6x+9.

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

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

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

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

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

Tehke korrutustehted võrrandis \left(x+1\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right).

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

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

$$\frac{8x}{\left(x-3\right)\left(x+3\right)^{2}}$$

Laiendage \left(x-3\right)\left(x+3\right)^{2}.

$$\frac{8x}{x^{3}+3x^{2}-9x-27}$$