Riješi (2/x+5+4/x+3)div(3x+13/x^2+3x+15)

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

Procijeni

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

Kratki koraci rješenja

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva x+5 i x+3 je \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}.

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

Pošto \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 imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Izvršite množenja u 2\left(x+3\right)+4\left(x+5\right).

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

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

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

Podijelite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} sa \frac{3x+13}{x^{2}+3x+15} tako što ćete pomnožiti \frac{6x+26}{\left(x+3\right)\left(x+5\right)} recipročnom vrijednošću od \frac{3x+13}{x^{2}+3x+15}.

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

Faktorirajte izraze koji nisu već faktorirani.

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

Otkaži 3x+13 u brojiocu i imeniocu.

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

Razvijte izraz.

$$\frac{2x^{2}+6x+30}{x^{2}+8x+15}$$

Proširi

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

Kratki koraci rješenja

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva x+5 i x+3 je \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}.

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

Pošto \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 imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Izvršite množenja u 2\left(x+3\right)+4\left(x+5\right).

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

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

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

Podijelite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} sa \frac{3x+13}{x^{2}+3x+15} tako što ćete pomnožiti \frac{6x+26}{\left(x+3\right)\left(x+5\right)} recipročnom vrijednošću od \frac{3x+13}{x^{2}+3x+15}.

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

Faktorirajte izraze koji nisu već faktorirani.

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

Otkaži 3x+13 u brojiocu i imeniocu.

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

Razvijte izraz.

$$\frac{2x^{2}+6x+30}{x^{2}+8x+15}$$