Rešite 10/x^2+6+9+2/x+3

$$\frac { 10 } { x ^ { 2 } + 6 + 9 } + \frac { 2 } { x + 3 }$$

Ovrednoti

$$\frac{2\left(x^{2}+5x+30\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

Kratka navodila za rešitev

Seštejte 6 in 9, da dobite 15.

$$\frac{10}{x^{2}+15}+\frac{2}{x+3}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x^{2}+15 in x+3 je \left(x+3\right)\left(x^{2}+15\right). Pomnožite \frac{10}{x^{2}+15} s/z \frac{x+3}{x+3}. Pomnožite \frac{2}{x+3} s/z \frac{x^{2}+15}{x^{2}+15}.

$$\frac{10\left(x+3\right)}{\left(x+3\right)\left(x^{2}+15\right)}+\frac{2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

\frac{10\left(x+3\right)}{\left(x+3\right)\left(x^{2}+15\right)} in \frac{2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{10\left(x+3\right)+2\left(x^{2}+15\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$

Izvedi množenje v 10\left(x+3\right)+2\left(x^{2}+15\right).

$$\frac{10x+30+2x^{2}+30}{\left(x+3\right)\left(x^{2}+15\right)}$$

Združite podobne člene v 10x+30+2x^{2}+30.

$$\frac{10x+60+2x^{2}}{\left(x+3\right)\left(x^{2}+15\right)}$$

Razčlenite \left(x+3\right)\left(x^{2}+15\right).

$$\frac{10x+60+2x^{2}}{x^{3}+3x^{2}+15x+45}$$

Faktoriziraj

$$\frac{2\left(x^{2}+5x+30\right)}{\left(x+3\right)\left(x^{2}+15\right)}$$