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\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-25x-72
Fattorizzare \left(2x^{2}+25x+72\right)x.
\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}
Per aggiungere o sottrarre espressioni, espandile per rendere uguali i denominatori. Moltiplica -2x^{2}-25x-72 per \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.
\frac{4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}
Poiché \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} e \frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} hanno lo stesso denominatore, calcolane l'addizione sommando i numeratori.
\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}
Esegui le moltiplicazioni in 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).
\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{x\left(x+8\right)\left(2x+9\right)}
Unisci i termini come in 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.
\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{2x^{3}+25x^{2}+72x}
Espandi x\left(x+8\right)\left(2x+9\right).
\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-25x-72
Fattorizzare \left(2x^{2}+25x+72\right)x.
\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}
Per aggiungere o sottrarre espressioni, espandile per rendere uguali i denominatori. Moltiplica -2x^{2}-25x-72 per \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.
\frac{4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}
Poiché \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} e \frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} hanno lo stesso denominatore, calcolane l'addizione sommando i numeratori.
\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}
Esegui le moltiplicazioni in 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).
\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{x\left(x+8\right)\left(2x+9\right)}
Unisci i termini come in 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.
\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{2x^{3}+25x^{2}+72x}
Espandi x\left(x+8\right)\left(2x+9\right).