Issolvi 7/x^2-4-5/x^2+4x+4

$$\frac { 7 } { x ^ { 2 } - 4 } - \frac { 5 } { x ^ { 2 } + 4 x + 4 }$$

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{2}-4. Iffattura x^{2}+4x+4.

$$\frac{7}{\left(x-2\right)\left(x+2\right)}-\frac{5}{\left(x+2\right)^{2}}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' \left(x-2\right)\left(x+2\right) u \left(x+2\right)^{2} huwa \left(x-2\right)\left(x+2\right)^{2}. Immultiplika \frac{7}{\left(x-2\right)\left(x+2\right)} b'\frac{x+2}{x+2}. Immultiplika \frac{5}{\left(x+2\right)^{2}} b'\frac{x-2}{x-2}.

$$\frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Billi \frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} u \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{7\left(x+2\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Agħmel il-multiplikazzjonijiet fi 7\left(x+2\right)-5\left(x-2\right).

$$\frac{7x+14-5x+10}{\left(x-2\right)\left(x+2\right)^{2}}$$

Ikkombina termini simili f'7x+14-5x+10.

$$\frac{2x+24}{\left(x-2\right)\left(x+2\right)^{2}}$$

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

$$\frac{2x+24}{x^{3}+2x^{2}-4x-8}$$

Iddifferenzja w.r.t. x

$$-\frac{\left(2x+17\right)^{2}-329}{\left(x-2\right)^{2}\left(x+2\right)^{3}}$$