Riješi -20/x^2+10x+24+x+16/x^2+11x+30

$$\frac { - 20 } { x ^ { 2 } + 10 x + 24 } + \frac { x + 16 } { x ^ { 2 } + 11 x + 30 }$$

Izračunaj

$$\frac{x-6}{\left(x+4\right)\left(x+5\right)}$$

Kratki koraci za rješenje

Rastavite x^{2}+10x+24 na faktore. Rastavite x^{2}+11x+30 na faktore.

$$\frac{-20}{\left(x+4\right)\left(x+6\right)}+\frac{x+16}{\left(x+5\right)\left(x+6\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+4\right)\left(x+6\right) i \left(x+5\right)\left(x+6\right) jest \left(x+4\right)\left(x+5\right)\left(x+6\right). Pomnožite \frac{-20}{\left(x+4\right)\left(x+6\right)} i \frac{x+5}{x+5}. Pomnožite \frac{x+16}{\left(x+5\right)\left(x+6\right)} i \frac{x+4}{x+4}.

$$\frac{-20\left(x+5\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Budući da \frac{-20\left(x+5\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)} i \frac{\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{-20\left(x+5\right)+\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Pomnožite izraz -20\left(x+5\right)+\left(x+16\right)\left(x+4\right).

$$\frac{-20x-100+x^{2}+4x+16x+64}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Kombinirajte slične izraze u -20x-100+x^{2}+4x+16x+64.

$$\frac{-36+x^{2}}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{-36+x^{2}}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}.

$$\frac{\left(x-6\right)\left(x+6\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Skratite x+6 u brojniku i nazivniku.

$$\frac{x-6}{\left(x+4\right)\left(x+5\right)}$$

Proširivanje broja \left(x+4\right)\left(x+5\right).

$$\frac{x-6}{x^{2}+9x+20}$$

Proširi

$$\frac{x-6}{\left(x+4\right)\left(x+5\right)}$$

Kratki koraci za rješenje

Rastavite x^{2}+10x+24 na faktore. Rastavite x^{2}+11x+30 na faktore.

$$\frac{-20}{\left(x+4\right)\left(x+6\right)}+\frac{x+16}{\left(x+5\right)\left(x+6\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+4\right)\left(x+6\right) i \left(x+5\right)\left(x+6\right) jest \left(x+4\right)\left(x+5\right)\left(x+6\right). Pomnožite \frac{-20}{\left(x+4\right)\left(x+6\right)} i \frac{x+5}{x+5}. Pomnožite \frac{x+16}{\left(x+5\right)\left(x+6\right)} i \frac{x+4}{x+4}.

$$\frac{-20\left(x+5\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Budući da \frac{-20\left(x+5\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)} i \frac{\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{-20\left(x+5\right)+\left(x+16\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Pomnožite izraz -20\left(x+5\right)+\left(x+16\right)\left(x+4\right).

$$\frac{-20x-100+x^{2}+4x+16x+64}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Kombinirajte slične izraze u -20x-100+x^{2}+4x+16x+64.

$$\frac{-36+x^{2}}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{-36+x^{2}}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}.

$$\frac{\left(x-6\right)\left(x+6\right)}{\left(x+4\right)\left(x+5\right)\left(x+6\right)}$$

Skratite x+6 u brojniku i nazivniku.

$$\frac{x-6}{\left(x+4\right)\left(x+5\right)}$$

Proširivanje broja \left(x+4\right)\left(x+5\right).

$$\frac{x-6}{x^{2}+9x+20}$$