Riješi 8/x+3+12/x+7/frac{5x+23{x^2+10x+21}}

$$\frac { \frac { 8 } { x + 3 } + \frac { 12 } { x + 7 } } { \frac { 5 x + 23 } { x ^ { 2 } + 10 x + 21 } }$$

Izračunaj

$$4$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+3 i x+7 jest \left(x+3\right)\left(x+7\right). Pomnožite \frac{8}{x+3} i \frac{x+7}{x+7}. Pomnožite \frac{12}{x+7} i \frac{x+3}{x+3}.

$$\frac{\frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)}+\frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Budući da \frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)} i \frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\frac{8\left(x+7\right)+12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Pomnožite izraz 8\left(x+7\right)+12\left(x+3\right).

$$\frac{\frac{8x+56+12x+36}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Kombinirajte slične izraze u 8x+56+12x+36.

$$\frac{\frac{20x+92}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Podijelite \frac{20x+92}{\left(x+3\right)\left(x+7\right)} s \frac{5x+23}{x^{2}+10x+21} tako da pomnožite \frac{20x+92}{\left(x+3\right)\left(x+7\right)} s brojem recipročnim broju \frac{5x+23}{x^{2}+10x+21}.

$$\frac{\left(20x+92\right)\left(x^{2}+10x+21\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{4\left(x+3\right)\left(x+7\right)\left(5x+23\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Skratite \left(x+3\right)\left(x+7\right)\left(5x+23\right) u brojniku i nazivniku.

$$4$$

Faktor

$$2^{2}$$