Rešite k/3k-8-4/k+2

$$\frac { k } { 3 k - 8 } - \frac { 4 } { k + 2 }$$

Ovrednoti

$$\frac{k^{2}-10k+32}{\left(3k-8\right)\left(k+2\right)}$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 3k-8 in k+2 je \left(3k-8\right)\left(k+2\right). Pomnožite \frac{k}{3k-8} s/z \frac{k+2}{k+2}. Pomnožite \frac{4}{k+2} s/z \frac{3k-8}{3k-8}.

$$\frac{k\left(k+2\right)}{\left(3k-8\right)\left(k+2\right)}-\frac{4\left(3k-8\right)}{\left(3k-8\right)\left(k+2\right)}$$

Ker \frac{k\left(k+2\right)}{\left(3k-8\right)\left(k+2\right)} in \frac{4\left(3k-8\right)}{\left(3k-8\right)\left(k+2\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{k\left(k+2\right)-4\left(3k-8\right)}{\left(3k-8\right)\left(k+2\right)}$$

Izvedi množenje v k\left(k+2\right)-4\left(3k-8\right).

$$\frac{k^{2}+2k-12k+32}{\left(3k-8\right)\left(k+2\right)}$$

Združite podobne člene v k^{2}+2k-12k+32.

$$\frac{k^{2}-10k+32}{\left(3k-8\right)\left(k+2\right)}$$

Razčlenite \left(3k-8\right)\left(k+2\right).

$$\frac{k^{2}-10k+32}{3k^{2}-2k-16}$$

Odvajajte w.r.t. k

$$\frac{28\left(k^{2}-8k+8\right)}{9k^{4}-12k^{3}-92k^{2}+64k+256}$$