Riješi 9y+3/y^2-11y+18+y+3/y-9

$$\frac { 9 y + 3 } { y ^ { 2 } - 11 y + 18 } + \frac { y + 3 } { y - 9 }$$

Izračunaj

$$\frac{y^{2}+10y-3}{\left(y-9\right)\left(y-2\right)}$$

Kratki koraci za rješenje

Rastavite y^{2}-11y+18 na faktore.

$$\frac{9y+3}{\left(y-9\right)\left(y-2\right)}+\frac{y+3}{y-9}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(y-9\right)\left(y-2\right) i y-9 jest \left(y-9\right)\left(y-2\right). Pomnožite \frac{y+3}{y-9} i \frac{y-2}{y-2}.

$$\frac{9y+3}{\left(y-9\right)\left(y-2\right)}+\frac{\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)}$$

Budući da \frac{9y+3}{\left(y-9\right)\left(y-2\right)} i \frac{\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{9y+3+\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)}$$

Pomnožite izraz 9y+3+\left(y+3\right)\left(y-2\right).

$$\frac{9y+3+y^{2}-2y+3y-6}{\left(y-9\right)\left(y-2\right)}$$

Kombinirajte slične izraze u 9y+3+y^{2}-2y+3y-6.

$$\frac{10y-3+y^{2}}{\left(y-9\right)\left(y-2\right)}$$

Proširivanje broja \left(y-9\right)\left(y-2\right).

$$\frac{10y-3+y^{2}}{y^{2}-11y+18}$$

Proširi

$$\frac{y^{2}+10y-3}{\left(y-9\right)\left(y-2\right)}$$

Kratki koraci za rješenje

Rastavite y^{2}-11y+18 na faktore.

$$\frac{9y+3}{\left(y-9\right)\left(y-2\right)}+\frac{y+3}{y-9}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(y-9\right)\left(y-2\right) i y-9 jest \left(y-9\right)\left(y-2\right). Pomnožite \frac{y+3}{y-9} i \frac{y-2}{y-2}.

$$\frac{9y+3}{\left(y-9\right)\left(y-2\right)}+\frac{\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)}$$

Budući da \frac{9y+3}{\left(y-9\right)\left(y-2\right)} i \frac{\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{9y+3+\left(y+3\right)\left(y-2\right)}{\left(y-9\right)\left(y-2\right)}$$

Pomnožite izraz 9y+3+\left(y+3\right)\left(y-2\right).

$$\frac{9y+3+y^{2}-2y+3y-6}{\left(y-9\right)\left(y-2\right)}$$

Kombinirajte slične izraze u 9y+3+y^{2}-2y+3y-6.

$$\frac{10y-3+y^{2}}{\left(y-9\right)\left(y-2\right)}$$

Proširivanje broja \left(y-9\right)\left(y-2\right).

$$\frac{10y-3+y^{2}}{y^{2}-11y+18}$$