Riješi x^2/x^2+6x+9-4/x^2-9=

$$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 } - \frac { 4 } { x ^ { 2 } - 9 } =$$

Procijeni

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

Kratki koraci rješenja

Faktorirajte x^{2}+6x+9. Faktorirajte x^{2}-9.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x+3\right)^{2} i \left(x-3\right)\left(x+3\right) je \left(x-3\right)\left(x+3\right)^{2}. Pomnožite \frac{x^{2}}{\left(x+3\right)^{2}} i \frac{x-3}{x-3}. Pomnožite \frac{4}{\left(x-3\right)\left(x+3\right)} i \frac{x+3}{x+3}.

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

Pošto \frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} i \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u x^{2}\left(x-3\right)-4\left(x+3\right).

$$\frac{x^{3}-3x^{2}-4x-12}{\left(x-3\right)\left(x+3\right)^{2}}$$

Proširite \left(x-3\right)\left(x+3\right)^{2}.

$$\frac{x^{3}-3x^{2}-4x-12}{x^{3}+3x^{2}-9x-27}$$

Razlikovanje u pogledu x

$$\frac{2x\left(3x^{2}-14x+39\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$