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\frac{2}{\left(x+2\right)\left(x-3\right)^{2}}-\frac{3x}{5\left(x^{2}-3\right)}
Aïlleu la x^{3}-4x^{2}-3x+18. Aïlleu la 5x^{2}-15.
\frac{2\times 5\left(x^{2}-3\right)}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)}-\frac{3x\left(x+2\right)\left(x-3\right)^{2}}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)}
Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. El mínim comú múltiple de \left(x+2\right)\left(x-3\right)^{2} i 5\left(x^{2}-3\right) és 5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right). Multipliqueu \frac{2}{\left(x+2\right)\left(x-3\right)^{2}} per \frac{5\left(x^{2}-3\right)}{5\left(x^{2}-3\right)}. Multipliqueu \frac{3x}{5\left(x^{2}-3\right)} per \frac{\left(x+2\right)\left(x-3\right)^{2}}{\left(x+2\right)\left(x-3\right)^{2}}.
\frac{2\times 5\left(x^{2}-3\right)-3x\left(x+2\right)\left(x-3\right)^{2}}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)}
Com que \frac{2\times 5\left(x^{2}-3\right)}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)} i \frac{3x\left(x+2\right)\left(x-3\right)^{2}}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)} tenen el mateix denominador, resteu-los mitjançant la subtracció dels seus numeradors.
\frac{10x^{2}-30-3x^{4}+18x^{3}-27x^{2}-6x^{3}+36x^{2}-54x}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)}
Feu les multiplicacions a 2\times 5\left(x^{2}-3\right)-3x\left(x+2\right)\left(x-3\right)^{2}.
\frac{19x^{2}-30-3x^{4}+12x^{3}-54x}{5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right)}
Combineu els termes similars de 10x^{2}-30-3x^{4}+18x^{3}-27x^{2}-6x^{3}+36x^{2}-54x.
\frac{19x^{2}-30-3x^{4}+12x^{3}-54x}{5x^{5}-20x^{4}-30x^{3}+150x^{2}+45x-270}
Expandiu 5\left(x+2\right)\left(x-3\right)^{2}\left(x^{2}-3\right).