Lahenda x^2/x^2+6x+9-4/x^2-9=

$$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 } - \frac { 4 } { x ^ { 2 } - 9 } =$$

Arvuta

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

Lühike lahenduskäik

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

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+3\right)^{2} ja \left(x-3\right)\left(x+3\right) vähim ühiskordne on \left(x-3\right)\left(x+3\right)^{2}. Korrutage omavahel \frac{x^{2}}{\left(x+3\right)^{2}} ja \frac{x-3}{x-3}. Korrutage omavahel \frac{4}{\left(x-3\right)\left(x+3\right)} ja \frac{x+3}{x+3}.

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

Kuna murdudel \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} ja \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} on sama nimetaja, lahutage nende lugejad.

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

Tehke korrutustehted võrrandis x^{2}\left(x-3\right)-4\left(x+3\right).

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

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

$$\frac{x^{3}-3x^{2}-4x-12}{x^{3}+3x^{2}-9x-27}$$

Diferentseeri x-i järgi

$$\frac{2x\left(3x^{2}-14x+39\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$