Lahenda 2/x^2+7x+10+3/x^2-25

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Arvuta

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Lühike lahenduskäik

Tegurda x^{2}+7x+10. Tegurda x^{2}-25.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+2\right)\left(x+5\right) ja \left(x-5\right)\left(x+5\right) vähim ühiskordne on \left(x-5\right)\left(x+2\right)\left(x+5\right). Korrutage omavahel \frac{2}{\left(x+2\right)\left(x+5\right)} ja \frac{x-5}{x-5}. Korrutage omavahel \frac{3}{\left(x-5\right)\left(x+5\right)} ja \frac{x+2}{x+2}.

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

Kuna murdudel \frac{2\left(x-5\right)}{\left(x-5\right)\left(x+2\right)\left(x+5\right)} ja \frac{3\left(x+2\right)}{\left(x-5\right)\left(x+2\right)\left(x+5\right)} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 2\left(x-5\right)+3\left(x+2\right).

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Kombineerige sarnased liikmed avaldises 2x-10+3x+6.

$$\frac{5x-4}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

Laiendage \left(x-5\right)\left(x+2\right)\left(x+5\right).

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

Diferentseeri x-i järgi

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$