Rešite 1/x^2-5x+6+1/x^2-3x+2+2/x^2-8x+15

$$\frac { 1 } { x ^ { 2 } - 5 x + 6 } + \frac { 1 } { x ^ { 2 } - 3 x + 2 } + \frac { 2 } { x ^ { 2 } - 8 x + 15 }$$

Ovrednoti

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

Kratka navodila za rešitev

Faktorizirajte x^{2}-5x+6. Faktorizirajte x^{2}-3x+2.

$$\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-2\right) in \left(x-2\right)\left(x-1\right) je \left(x-3\right)\left(x-2\right)\left(x-1\right). Pomnožite \frac{1}{\left(x-3\right)\left(x-2\right)} s/z \frac{x-1}{x-1}. Pomnožite \frac{1}{\left(x-2\right)\left(x-1\right)} s/z \frac{x-3}{x-3}.

$$\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)} in \frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{x-1+x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Združite podobne člene v x-1+x-3.

$$\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}.

$$\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Okrajšaj x-2 v števcu in imenovalcu.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Faktorizirajte x^{2}-8x+15.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x-1\right) in \left(x-5\right)\left(x-3\right) je \left(x-5\right)\left(x-3\right)\left(x-1\right). Pomnožite \frac{2}{\left(x-3\right)\left(x-1\right)} s/z \frac{x-5}{x-5}. Pomnožite \frac{2}{\left(x-5\right)\left(x-3\right)} s/z \frac{x-1}{x-1}.

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

\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} in \frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v 2\left(x-5\right)+2\left(x-1\right).

$$\frac{2x-10+2x-2}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Združite podobne člene v 2x-10+2x-2.

$$\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}.

$$\frac{4\left(x-3\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Okrajšaj x-3 v števcu in imenovalcu.

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

Razčlenite \left(x-5\right)\left(x-1\right).

$$\frac{4}{x^{2}-6x+5}$$

Odvajajte w.r.t. x

$$\frac{8\left(3-x\right)}{\left(\left(x-5\right)\left(x-1\right)\right)^{2}}$$