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

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

Evaluer

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

Korte løsningstrin

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

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

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Multiplicer -2x^{2}-25x-72 gange \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

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

Da \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} og \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)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.

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

Lav multiplikationerne i 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).

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

Kombiner ens led i 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.

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

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

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

Udvid

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

Korte løsningstrin

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

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

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Multiplicer -2x^{2}-25x-72 gange \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

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

Da \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} og \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)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.

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

Lav multiplikationerne i 4x^{2}+9x+16+\left(-2x^{2}-25x-72\right)x\left(x+8\right)\left(2x+9\right).

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

Kombiner ens led i 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-50x^{4}-625x^{3}-1800x^{2}-144x^{3}-1800x^{2}-5184x.

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

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

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