Riješi 2/x+5+4/x+3/frac{3x+13{x^2+8x+15}}

$$\frac { \frac { 2 } { x + 5 } + \frac { 4 } { x + 3 } } { \frac { 3 x + 13 } { x ^ { 2 } + 8 x + 15 } }$$

Izračunaj

$$2$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+5 i x+3 jest \left(x+3\right)\left(x+5\right). Pomnožite \frac{2}{x+5} i \frac{x+3}{x+3}. Pomnožite \frac{4}{x+3} i \frac{x+5}{x+5}.

$$\frac{\frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}+\frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Budući da \frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)} i \frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\frac{2\left(x+3\right)+4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Pomnožite izraz 2\left(x+3\right)+4\left(x+5\right).

$$\frac{\frac{2x+6+4x+20}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Kombinirajte slične izraze u 2x+6+4x+20.

$$\frac{\frac{6x+26}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Podijelite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} s \frac{3x+13}{x^{2}+8x+15} tako da pomnožite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} s brojem recipročnim broju \frac{3x+13}{x^{2}+8x+15}.

$$\frac{\left(6x+26\right)\left(x^{2}+8x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{2\left(x+3\right)\left(x+5\right)\left(3x+13\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Skratite \left(x+3\right)\left(x+5\right)\left(3x+13\right) u brojniku i nazivniku.

$$2$$

Faktor

$$2$$