Rešite 8/x^2-9-5/x^2+6x+9

$$\frac { 8 } { x ^ { 2 } - 9 } - \frac { 5 } { x ^ { 2 } + 6 x + 9 }$$

Ovrednoti

$$\frac{3\left(x+13\right)}{\left(x-3\right)\left(x+3\right)^{2}}$$

Kratka navodila za rešitev

Faktorizirajte x^{2}-9. Faktorizirajte x^{2}+6x+9.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-3\right)\left(x+3\right) in \left(x+3\right)^{2} je \left(x-3\right)\left(x+3\right)^{2}. Pomnožite \frac{8}{\left(x-3\right)\left(x+3\right)} s/z \frac{x+3}{x+3}. Pomnožite \frac{5}{\left(x+3\right)^{2}} s/z \frac{x-3}{x-3}.

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

Ker \frac{8\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} in \frac{5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v 8\left(x+3\right)-5\left(x-3\right).

$$\frac{8x+24-5x+15}{\left(x-3\right)\left(x+3\right)^{2}}$$

Združite podobne člene v 8x+24-5x+15.

$$\frac{3x+39}{\left(x-3\right)\left(x+3\right)^{2}}$$

Razčlenite \left(x-3\right)\left(x+3\right)^{2}.

$$\frac{3x+39}{x^{3}+3x^{2}-9x-27}$$

Odvajajte w.r.t. x

$$-\frac{6\left(\left(x+9\right)^{2}-96\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$