Rešite 7/x^2-4-5/x^2+4x+4

$$\frac { 7 } { x ^ { 2 } - 4 } - \frac { 5 } { x ^ { 2 } + 4 x + 4 }$$

Ovrednoti

$$\frac{2\left(x+12\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Kratka navodila za rešitev

Faktorizirajte x^{2}-4. Faktorizirajte x^{2}+4x+4.

$$\frac{7}{\left(x-2\right)\left(x+2\right)}-\frac{5}{\left(x+2\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-2\right)\left(x+2\right) in \left(x+2\right)^{2} je \left(x-2\right)\left(x+2\right)^{2}. Pomnožite \frac{7}{\left(x-2\right)\left(x+2\right)} s/z \frac{x+2}{x+2}. Pomnožite \frac{5}{\left(x+2\right)^{2}} s/z \frac{x-2}{x-2}.

$$\frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Ker \frac{7\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} in \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{7\left(x+2\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Izvedi množenje v 7\left(x+2\right)-5\left(x-2\right).

$$\frac{7x+14-5x+10}{\left(x-2\right)\left(x+2\right)^{2}}$$

Združite podobne člene v 7x+14-5x+10.

$$\frac{2x+24}{\left(x-2\right)\left(x+2\right)^{2}}$$

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

$$\frac{2x+24}{x^{3}+2x^{2}-4x-8}$$

Odvajajte w.r.t. x

$$-\frac{\left(2x+17\right)^{2}-329}{\left(x-2\right)^{2}\left(x+2\right)^{3}}$$