Réitigh 8/x^2-9-5/x^2+6x+9

$$\frac { 8 } { x ^ { 2 } - 9 } - \frac { 5 } { x ^ { 2 } + 6 x + 9 }$$

Luacháil

$$\frac{3\left(x+13\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Céimeanna gearra réitigh

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

$$\frac{8}{\left(x-3\right)\left(x+3\right)}-\frac{5}{\left(x+3\right)^{2}}$$

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)\left(x+3\right) agus \left(x+3\right)^{2} ná \left(x-3\right)\left(x+3\right)^{2}. Méadaigh \frac{8}{\left(x-3\right)\left(x+3\right)} faoi \frac{x+3}{x+3}. Méadaigh \frac{5}{\left(x+3\right)^{2}} faoi \frac{x-3}{x-3}.

$$\frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}}-\frac{5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Tá an t-ainmneoir céanna ag \frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} agus \frac{5\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.

$$\frac{8\left(x+3\right)-5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Déan iolrúcháin in 8\left(x+3\right)-5\left(x-3\right).

$$\frac{8x+24-5x+15}{\left(x-3\right)\left(x+3\right)^{2}}$$

Cumaisc téarmaí comhchosúla in: 8x+24-5x+15.

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

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

$$\frac{3x+39}{x^{3}+3x^{2}-9x-27}$$

Difreálaigh w.r.t. x

$$-\frac{6\left(\left(x+9\right)^{2}-96\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$