Rešite 8/x+3+12/x+7/frac{5x+23{x^2+10x+21}}

$$\frac { \frac { 8 } { x + 3 } + \frac { 12 } { x + 7 } } { \frac { 5 x + 23 } { x ^ { 2 } + 10 x + 21 } }$$

Ovrednoti

$$4$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+3 in x+7 je \left(x+3\right)\left(x+7\right). Pomnožite \frac{8}{x+3} s/z \frac{x+7}{x+7}. Pomnožite \frac{12}{x+7} s/z \frac{x+3}{x+3}.

$$\frac{\frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)}+\frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

\frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)} in \frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{8\left(x+7\right)+12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Izvedi množenje v 8\left(x+7\right)+12\left(x+3\right).

$$\frac{\frac{8x+56+12x+36}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Združite podobne člene v 8x+56+12x+36.

$$\frac{\frac{20x+92}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Delite \frac{20x+92}{\left(x+3\right)\left(x+7\right)} s/z \frac{5x+23}{x^{2}+10x+21} tako, da pomnožite \frac{20x+92}{\left(x+3\right)\left(x+7\right)} z obratno vrednostjo \frac{5x+23}{x^{2}+10x+21}.

$$\frac{\left(20x+92\right)\left(x^{2}+10x+21\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{4\left(x+3\right)\left(x+7\right)\left(5x+23\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Okrajšaj \left(x+3\right)\left(x+7\right)\left(5x+23\right) v števcu in imenovalcu.

$$4$$

Faktoriziraj

$$2^{2}$$