Lahenda 4x^2+9x+16/left(2x^2+25x+72right)x-2x^2-25x-72

$$\frac{ 4 { x }^{ 2 } +9x+16 }{ \left( 2 { x }^{ 2 } +25x+72 \right) x } -2 { x }^{ 2 } -25x-72$$

Arvuta

$$\frac{16-5175x-3596x^{2}-913x^{3}-100x^{4}-4x^{5}}{x\left(x+8\right)\left(2x+9\right)}$$

Lühike lahenduskäik

Tegurda \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-25x-72$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel -2x^{2}-25x-72 ja \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Kuna murdudel \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} ja \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)} on sama nimetaja, liitke nende lugejad.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Tehke korrutustehted võrrandis 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Kombineerige sarnased liikmed avaldises 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

Laiendage x\left(x+8\right)\left(2x+9\right).

$$\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{2x^{3}+25x^{2}+72x}$$

Laienda

$$\frac{16-5175x-3596x^{2}-913x^{3}-100x^{4}-4x^{5}}{x\left(2x^{2}+25x+72\right)}$$

Lühike lahenduskäik

Tegurda \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-25x-72$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel -2x^{2}-25x-72 ja \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Kuna murdudel \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} ja \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)} on sama nimetaja, liitke nende lugejad.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Tehke korrutustehted võrrandis 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Kombineerige sarnased liikmed avaldises 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

Laiendage x\left(x+8\right)\left(2x+9\right).

$$\frac{-3596x^{2}-5175x+16-4x^{5}-100x^{4}-913x^{3}}{2x^{3}+25x^{2}+72x}$$