Issolvi 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Evalwa

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iffattura x^{2}+7x+10. Iffattura x^{2}-25.

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

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+5\right) u \left(x-5\right)\left(x+5\right) huwa \left(x-5\right)\left(x+2\right)\left(x+5\right). Immultiplika \frac{2}{\left(x+2\right)\left(x+5\right)} b'\frac{x-5}{x-5}. Immultiplika \frac{3}{\left(x-5\right)\left(x+5\right)} b'\frac{x+2}{x+2}.

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

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

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

Agħmel il-multiplikazzjonijiet fi 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Ikkombina termini simili f'2x-10+3x+6.

$$\frac{5x-4}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Espandi \left(x-5\right)\left(x+2\right)\left(x+5\right).

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Iddifferenzja w.r.t. x

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$