Réitigh x^2/x^2+6x+9-4/x^2-9=

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

Luacháil

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

Céimeanna gearra réitigh

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

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

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x+3\right)^{2} agus \left(x-3\right)\left(x+3\right) ná \left(x-3\right)\left(x+3\right)^{2}. Méadaigh \frac{x^{2}}{\left(x+3\right)^{2}} faoi \frac{x-3}{x-3}. Méadaigh \frac{4}{\left(x-3\right)\left(x+3\right)} faoi \frac{x+3}{x+3}.

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

Tá an t-ainmneoir céanna ag \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} agus \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Déan iolrúcháin in x^{2}\left(x-3\right)-4\left(x+3\right).

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

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

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

Difreálaigh w.r.t. x

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