Riješi x+2/x^2-16+4/5x^2-19x-4

$$\frac { x + 2 } { x ^ { 2 } - 16 } + \frac { 4 } { 5 x ^ { 2 } - 19 x - 4 }$$

Procijeni

$$\frac{5x^{2}+15x+18}{\left(5x+1\right)\left(x^{2}-16\right)}$$

Kratki koraci rješenja

Faktorirajte x^{2}-16. Faktorirajte 5x^{2}-19x-4.

$$\frac{x+2}{\left(x-4\right)\left(x+4\right)}+\frac{4}{\left(x-4\right)\left(5x+1\right)}$$

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x-4\right)\left(x+4\right) i \left(x-4\right)\left(5x+1\right) je \left(x-4\right)\left(x+4\right)\left(5x+1\right). Pomnožite \frac{x+2}{\left(x-4\right)\left(x+4\right)} i \frac{5x+1}{5x+1}. Pomnožite \frac{4}{\left(x-4\right)\left(5x+1\right)} i \frac{x+4}{x+4}.

$$\frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}+\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Pošto \frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} i \frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{\left(x+2\right)\left(5x+1\right)+4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Izvršite množenja u \left(x+2\right)\left(5x+1\right)+4\left(x+4\right).

$$\frac{5x^{2}+x+10x+2+4x+16}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Kombinirajte slične izraze u 5x^{2}+x+10x+2+4x+16.

$$\frac{5x^{2}+15x+18}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Proširite \left(x-4\right)\left(x+4\right)\left(5x+1\right).

$$\frac{5x^{2}+15x+18}{5x^{3}+x^{2}-80x-16}$$

Proširi

$$\frac{5x^{2}+15x+18}{\left(5x+1\right)\left(x^{2}-16\right)}$$

Kratki koraci rješenja

Faktorirajte x^{2}-16. Faktorirajte 5x^{2}-19x-4.

$$\frac{x+2}{\left(x-4\right)\left(x+4\right)}+\frac{4}{\left(x-4\right)\left(5x+1\right)}$$

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x-4\right)\left(x+4\right) i \left(x-4\right)\left(5x+1\right) je \left(x-4\right)\left(x+4\right)\left(5x+1\right). Pomnožite \frac{x+2}{\left(x-4\right)\left(x+4\right)} i \frac{5x+1}{5x+1}. Pomnožite \frac{4}{\left(x-4\right)\left(5x+1\right)} i \frac{x+4}{x+4}.

$$\frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}+\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Pošto \frac{\left(x+2\right)\left(5x+1\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} i \frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{\left(x+2\right)\left(5x+1\right)+4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Izvršite množenja u \left(x+2\right)\left(5x+1\right)+4\left(x+4\right).

$$\frac{5x^{2}+x+10x+2+4x+16}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Kombinirajte slične izraze u 5x^{2}+x+10x+2+4x+16.

$$\frac{5x^{2}+15x+18}{\left(x-4\right)\left(x+4\right)\left(5x+1\right)}$$

Proširite \left(x-4\right)\left(x+4\right)\left(5x+1\right).

$$\frac{5x^{2}+15x+18}{5x^{3}+x^{2}-80x-16}$$