Rešite 2/x+5+4/x+3/frac{3x+13{x^2+8x+15}}

$$\frac { \frac { 2 } { x + 5 } + \frac { 4 } { x + 3 } } { \frac { 3 x + 13 } { x ^ { 2 } + 8 x + 15 } }$$

Ovrednoti

$$2$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+5 in x+3 je \left(x+3\right)\left(x+5\right). Pomnožite \frac{2}{x+5} s/z \frac{x+3}{x+3}. Pomnožite \frac{4}{x+3} s/z \frac{x+5}{x+5}.

$$\frac{\frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}+\frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

\frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)} in \frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{2\left(x+3\right)+4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Izvedi množenje v 2\left(x+3\right)+4\left(x+5\right).

$$\frac{\frac{2x+6+4x+20}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Združite podobne člene v 2x+6+4x+20.

$$\frac{\frac{6x+26}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+8x+15}}$$

Delite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} s/z \frac{3x+13}{x^{2}+8x+15} tako, da pomnožite \frac{6x+26}{\left(x+3\right)\left(x+5\right)} z obratno vrednostjo \frac{3x+13}{x^{2}+8x+15}.

$$\frac{\left(6x+26\right)\left(x^{2}+8x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{2\left(x+3\right)\left(x+5\right)\left(3x+13\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Okrajšaj \left(x+3\right)\left(x+5\right)\left(3x+13\right) v števcu in imenovalcu.

$$2$$

Faktoriziraj

$$2$$