Rešite 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Ovrednoti

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Kratka navodila za rešitev

Faktorizirajte x^{2}+7x+10. Faktorizirajte x^{2}-25.

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

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

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

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

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

Izvedi množenje v 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Združite podobne člene v 2x-10+3x+6.

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

Razčlenite \left(x-5\right)\left(x+2\right)\left(x+5\right).

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Odvajajte w.r.t. x

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$