Riješi 1/a-5+a/a^2-4a-5+a+3/a^2+2a+1

$$\frac { 1 } { a - 5 } + \frac { a } { a ^ { 2 } - 4 a - 5 } + \frac { a + 3 } { a ^ { 2 } + 2 a + 1 }$$

Izračunaj

$$\frac{\left(a-2\right)\left(3a+7\right)}{\left(a-5\right)\left(a+1\right)^{2}}$$

Kratki koraci za rješenje

Rastavite a^{2}-4a-5 na faktore.

$$\frac{1}{a-5}+\frac{a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva a-5 i \left(a-5\right)\left(a+1\right) jest \left(a-5\right)\left(a+1\right). Pomnožite \frac{1}{a-5} i \frac{a+1}{a+1}.

$$\frac{a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Budući da \frac{a+1}{\left(a-5\right)\left(a+1\right)} i \frac{a}{\left(a-5\right)\left(a+1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{a+1+a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Kombinirajte slične izraze u a+1+a.

$$\frac{2a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Rastavite a^{2}+2a+1 na faktore.

$$\frac{2a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{\left(a+1\right)^{2}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(a-5\right)\left(a+1\right) i \left(a+1\right)^{2} jest \left(a-5\right)\left(a+1\right)^{2}. Pomnožite \frac{2a+1}{\left(a-5\right)\left(a+1\right)} i \frac{a+1}{a+1}. Pomnožite \frac{a+3}{\left(a+1\right)^{2}} i \frac{a-5}{a-5}.

$$\frac{\left(2a+1\right)\left(a+1\right)}{\left(a-5\right)\left(a+1\right)^{2}}+\frac{\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}}$$

Budući da \frac{\left(2a+1\right)\left(a+1\right)}{\left(a-5\right)\left(a+1\right)^{2}} i \frac{\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(2a+1\right)\left(a+1\right)+\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}}$$

Pomnožite izraz \left(2a+1\right)\left(a+1\right)+\left(a+3\right)\left(a-5\right).

$$\frac{2a^{2}+2a+a+1+a^{2}-5a+3a-15}{\left(a-5\right)\left(a+1\right)^{2}}$$

Kombinirajte slične izraze u 2a^{2}+2a+a+1+a^{2}-5a+3a-15.

$$\frac{3a^{2}+a-14}{\left(a-5\right)\left(a+1\right)^{2}}$$

Proširivanje broja \left(a-5\right)\left(a+1\right)^{2}.

$$\frac{3a^{2}+a-14}{a^{3}-3a^{2}-9a-5}$$

Proširi

$$\frac{3a^{2}+a-14}{\left(a-5\right)\left(a+1\right)^{2}}$$

Kratki koraci za rješenje

Rastavite a^{2}-4a-5 na faktore.

$$\frac{1}{a-5}+\frac{a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva a-5 i \left(a-5\right)\left(a+1\right) jest \left(a-5\right)\left(a+1\right). Pomnožite \frac{1}{a-5} i \frac{a+1}{a+1}.

$$\frac{a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Budući da \frac{a+1}{\left(a-5\right)\left(a+1\right)} i \frac{a}{\left(a-5\right)\left(a+1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{a+1+a}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Kombinirajte slične izraze u a+1+a.

$$\frac{2a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{a^{2}+2a+1}$$

Rastavite a^{2}+2a+1 na faktore.

$$\frac{2a+1}{\left(a-5\right)\left(a+1\right)}+\frac{a+3}{\left(a+1\right)^{2}}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(a-5\right)\left(a+1\right) i \left(a+1\right)^{2} jest \left(a-5\right)\left(a+1\right)^{2}. Pomnožite \frac{2a+1}{\left(a-5\right)\left(a+1\right)} i \frac{a+1}{a+1}. Pomnožite \frac{a+3}{\left(a+1\right)^{2}} i \frac{a-5}{a-5}.

$$\frac{\left(2a+1\right)\left(a+1\right)}{\left(a-5\right)\left(a+1\right)^{2}}+\frac{\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}}$$

Budući da \frac{\left(2a+1\right)\left(a+1\right)}{\left(a-5\right)\left(a+1\right)^{2}} i \frac{\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\left(2a+1\right)\left(a+1\right)+\left(a+3\right)\left(a-5\right)}{\left(a-5\right)\left(a+1\right)^{2}}$$

Pomnožite izraz \left(2a+1\right)\left(a+1\right)+\left(a+3\right)\left(a-5\right).

$$\frac{2a^{2}+2a+a+1+a^{2}-5a+3a-15}{\left(a-5\right)\left(a+1\right)^{2}}$$

Kombinirajte slične izraze u 2a^{2}+2a+a+1+a^{2}-5a+3a-15.

$$\frac{3a^{2}+a-14}{\left(a-5\right)\left(a+1\right)^{2}}$$

Proširivanje broja \left(a-5\right)\left(a+1\right)^{2}.

$$\frac{3a^{2}+a-14}{a^{3}-3a^{2}-9a-5}$$