Issolvi 8/x^2-9-5/x^2+6x+9

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

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

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x-3\right)\left(x+3\right) u \left(x+3\right)^{2} huwa \left(x-3\right)\left(x+3\right)^{2}. Immultiplika \frac{8}{\left(x-3\right)\left(x+3\right)} b'\frac{x+3}{x+3}. Immultiplika \frac{5}{\left(x+3\right)^{2}} b'\frac{x-3}{x-3}.

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

Billi \frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} u \frac{5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Agħmel il-multiplikazzjonijiet fi 8\left(x+3\right)-5\left(x-3\right).

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

Ikkombina termini simili f'8x+24-5x+15.

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

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

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

Iddifferenzja w.r.t. x

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