Løs 2x^2+9x+2x^2+16/(2x^2+9x+16x+72)x-2x^2+16x+7x+72/1=

$$\frac { 2 x ^ { 2 } + 9 x + 2 x ^ { 2 } + 16 } { ( 2 x ^ { 2 } + 9 x + 16 x + 72 ) x } - \frac { 2 x ^ { 2 } + 16 x + 7 x + 72 } { 1 } =$$

Evaluer

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(x+8\right)\left(2x+9\right)}$$

Korte løsningstrin

Kombiner 2x^{2} og 2x^{2} for at få 4x^{2}.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Kombiner 9x og 16x for at få 25x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Kombiner 16x og 7x for at få 23x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Hvad som helst divideret med én er lig med sig selv.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

For at finde det modsatte af 2x^{2}+23x+72 skal du finde det modsatte af hvert led.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

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

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Multiplicer -2x^{2}-23x-72 gange \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Da \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} og \frac{\left(-2x^{2}-23x-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.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Lav multiplikationerne i 4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Kombiner ens led i 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

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

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$

Udvid

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(2x^{2}+25x+72\right)}$$

Korte løsningstrin

Kombiner 2x^{2} og 2x^{2} for at få 4x^{2}.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Kombiner 9x og 16x for at få 25x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Kombiner 16x og 7x for at få 23x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Hvad som helst divideret med én er lig med sig selv.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

For at finde det modsatte af 2x^{2}+23x+72 skal du finde det modsatte af hvert led.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

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

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Multiplicer -2x^{2}-23x-72 gange \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Da \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} og \frac{\left(-2x^{2}-23x-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.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Lav multiplikationerne i 4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Kombiner ens led i 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

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

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$