Riješi x-10/x+15+x-10/x-5/1-frac{5{x-5}}

$$\frac { \frac { x - 10 } { x + 15 } + \frac { x - 10 } { x - 5 } } { 1 - \frac { 5 } { x - 5 } }$$

Izračunaj

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+15 i x-5 jest \left(x-5\right)\left(x+15\right). Pomnožite \frac{x-10}{x+15} i \frac{x-5}{x-5}. Pomnožite \frac{x-10}{x-5} i \frac{x+15}{x+15}.

$$\frac{\frac{\left(x-10\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)}+\frac{\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Budući da \frac{\left(x-10\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)} i \frac{\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\frac{\left(x-10\right)\left(x-5\right)+\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Pomnožite izraz \left(x-10\right)\left(x-5\right)+\left(x-10\right)\left(x+15\right).

$$\frac{\frac{x^{2}-5x-10x+50+x^{2}+15x-10x-150}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Kombinirajte slične izraze u x^{2}-5x-10x+50+x^{2}+15x-10x-150.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Pomnožite 1 i \frac{x-5}{x-5}.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-5}{x-5}-\frac{5}{x-5}}$$

Budući da \frac{x-5}{x-5} i \frac{5}{x-5} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-5-5}{x-5}}$$

Kombinirajte slične izraze u x-5-5.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-10}{x-5}}$$

Podijelite \frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)} s \frac{x-10}{x-5} tako da pomnožite \frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)} s brojem recipročnim broju \frac{x-10}{x-5}.

$$\frac{\left(2x^{2}-10x-100\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)\left(x-10\right)}$$

Skratite x-5 u brojniku i nazivniku.

$$\frac{2x^{2}-10x-100}{\left(x-10\right)\left(x+15\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{2\left(x-10\right)\left(x+5\right)}{\left(x-10\right)\left(x+15\right)}$$

Skratite x-10 u brojniku i nazivniku.

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

Proširite izraz.

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

Proširi

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+15 i x-5 jest \left(x-5\right)\left(x+15\right). Pomnožite \frac{x-10}{x+15} i \frac{x-5}{x-5}. Pomnožite \frac{x-10}{x-5} i \frac{x+15}{x+15}.

$$\frac{\frac{\left(x-10\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)}+\frac{\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Budući da \frac{\left(x-10\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)} i \frac{\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\frac{\left(x-10\right)\left(x-5\right)+\left(x-10\right)\left(x+15\right)}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Pomnožite izraz \left(x-10\right)\left(x-5\right)+\left(x-10\right)\left(x+15\right).

$$\frac{\frac{x^{2}-5x-10x+50+x^{2}+15x-10x-150}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Kombinirajte slične izraze u x^{2}-5x-10x+50+x^{2}+15x-10x-150.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{1-\frac{5}{x-5}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Pomnožite 1 i \frac{x-5}{x-5}.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-5}{x-5}-\frac{5}{x-5}}$$

Budući da \frac{x-5}{x-5} i \frac{5}{x-5} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-5-5}{x-5}}$$

Kombinirajte slične izraze u x-5-5.

$$\frac{\frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)}}{\frac{x-10}{x-5}}$$

Podijelite \frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)} s \frac{x-10}{x-5} tako da pomnožite \frac{2x^{2}-10x-100}{\left(x-5\right)\left(x+15\right)} s brojem recipročnim broju \frac{x-10}{x-5}.

$$\frac{\left(2x^{2}-10x-100\right)\left(x-5\right)}{\left(x-5\right)\left(x+15\right)\left(x-10\right)}$$

Skratite x-5 u brojniku i nazivniku.

$$\frac{2x^{2}-10x-100}{\left(x-10\right)\left(x+15\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{2\left(x-10\right)\left(x+5\right)}{\left(x-10\right)\left(x+15\right)}$$

Skratite x-10 u brojniku i nazivniku.

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

Proširite izraz.

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