Riješi x^2+8xdiv(x^2-9)

$${ x }^{ 2 } +8x \div ( { x }^{ 2 } -9)$$

Procijeni

$$\frac{x\left(x-1\right)\left(x^{2}+x-8\right)}{x^{2}-9}$$

Kratki koraci rješenja

Faktorirajte x^{2}-9.

$$x^{2}+\frac{8x}{\left(x-3\right)\left(x+3\right)}$$

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Pomnožite x^{2} i \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.

$$\frac{x^{2}\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{8x}{\left(x-3\right)\left(x+3\right)}$$

Pošto \frac{x^{2}\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} i \frac{8x}{\left(x-3\right)\left(x+3\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{x^{2}\left(x-3\right)\left(x+3\right)+8x}{\left(x-3\right)\left(x+3\right)}$$

Izvršite množenja u x^{2}\left(x-3\right)\left(x+3\right)+8x.

$$\frac{x^{4}+3x^{3}-3x^{3}-9x^{2}+8x}{\left(x-3\right)\left(x+3\right)}$$

Kombinirajte slične izraze u x^{4}+3x^{3}-3x^{3}-9x^{2}+8x.

$$\frac{x^{4}-9x^{2}+8x}{\left(x-3\right)\left(x+3\right)}$$

Proširite \left(x-3\right)\left(x+3\right).

$$\frac{x^{4}-9x^{2}+8x}{x^{2}-9}$$

Faktor

$$\frac{x\left(x-1\right)\left(x^{2}+x-8\right)}{x^{2}-9}$$