Riješi (x+4y/x^{2-4xy}-x-4y/x^2+4xy):4y^2/x^2-16y^2

$$( \frac { x + 4 y } { x ^ { 2 } - 4 x y } - \frac { x - 4 y } { x ^ { 2 } + 4 x y } ) : \frac { 4 y ^ { 2 } } { x ^ { 2 } - 16 y ^ { 2 } }$$

Izračunaj

$$\frac{4}{y}$$

Kratki koraci za rješenje

Rastavite x^{2}-4xy na faktore. Rastavite x^{2}+4xy na faktore.

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

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

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

Budući da \frac{\left(x+4y\right)\left(x+4y\right)}{x\left(x-4y\right)\left(x+4y\right)} i \frac{\left(x-4y\right)\left(x-4y\right)}{x\left(x-4y\right)\left(x+4y\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(x+4y\right)\left(x+4y\right)-\left(x-4y\right)\left(x-4y\right).

$$\frac{\frac{x^{2}+4xy+4xy+16y^{2}-x^{2}+4xy+4xy-16y^{2}}{x\left(x-4y\right)\left(x+4y\right)}}{\frac{4y^{2}}{x^{2}-16y^{2}}}$$

Kombinirajte slične izraze u x^{2}+4xy+4xy+16y^{2}-x^{2}+4xy+4xy-16y^{2}.

$$\frac{\frac{16xy}{x\left(x-4y\right)\left(x+4y\right)}}{\frac{4y^{2}}{x^{2}-16y^{2}}}$$

Skratite x u brojniku i nazivniku.

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

Podijelite \frac{16y}{\left(x-4y\right)\left(x+4y\right)} s \frac{4y^{2}}{x^{2}-16y^{2}} tako da pomnožite \frac{16y}{\left(x-4y\right)\left(x+4y\right)} s brojem recipročnim broju \frac{4y^{2}}{x^{2}-16y^{2}}.

$$\frac{16y\left(x^{2}-16y^{2}\right)}{\left(x-4y\right)\left(x+4y\right)\times 4y^{2}}$$

Skratite 4y u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{4\left(x-4y\right)\left(x+4y\right)}{y\left(x-4y\right)\left(x+4y\right)}$$

Skratite \left(x-4y\right)\left(x+4y\right) u brojniku i nazivniku.

$$\frac{4}{y}$$

Proširi

$$\frac{4}{y}$$

Kratki koraci za rješenje

Rastavite x^{2}-4xy na faktore. Rastavite x^{2}+4xy na faktore.

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

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

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

Budući da \frac{\left(x+4y\right)\left(x+4y\right)}{x\left(x-4y\right)\left(x+4y\right)} i \frac{\left(x-4y\right)\left(x-4y\right)}{x\left(x-4y\right)\left(x+4y\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(x+4y\right)\left(x+4y\right)-\left(x-4y\right)\left(x-4y\right).

$$\frac{\frac{x^{2}+4xy+4xy+16y^{2}-x^{2}+4xy+4xy-16y^{2}}{x\left(x-4y\right)\left(x+4y\right)}}{\frac{4y^{2}}{x^{2}-16y^{2}}}$$

Kombinirajte slične izraze u x^{2}+4xy+4xy+16y^{2}-x^{2}+4xy+4xy-16y^{2}.

$$\frac{\frac{16xy}{x\left(x-4y\right)\left(x+4y\right)}}{\frac{4y^{2}}{x^{2}-16y^{2}}}$$

Skratite x u brojniku i nazivniku.

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

Podijelite \frac{16y}{\left(x-4y\right)\left(x+4y\right)} s \frac{4y^{2}}{x^{2}-16y^{2}} tako da pomnožite \frac{16y}{\left(x-4y\right)\left(x+4y\right)} s brojem recipročnim broju \frac{4y^{2}}{x^{2}-16y^{2}}.

$$\frac{16y\left(x^{2}-16y^{2}\right)}{\left(x-4y\right)\left(x+4y\right)\times 4y^{2}}$$

Skratite 4y u brojniku i nazivniku.

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

Rastavite na faktore izraze koji još nisu rastavljeni na faktore.

$$\frac{4\left(x-4y\right)\left(x+4y\right)}{y\left(x-4y\right)\left(x+4y\right)}$$

Skratite \left(x-4y\right)\left(x+4y\right) u brojniku i nazivniku.

$$\frac{4}{y}$$