Issolvi ((-11)+1)div(sqrt{8-11}-3)

$$((-11)+1) \div ( \sqrt{ 8-11 } -3)$$

Evalwa

$$\text{Indeterminate}$$

Passi tas-Soluzzjonijiet

Żid -11 u 1 biex tikseb -10.

$$\frac{-10}{\sqrt{8-11}-3}$$

Naqqas 11 minn 8 biex tikseb -3.

$$\frac{-10}{\sqrt{-3}-3}$$

Irrazzjonalizza d-denominatur tal-\frac{-10}{\sqrt{-3}-3} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{-3}+3.

$$\frac{-10\left(\sqrt{-3}+3\right)}{\left(\sqrt{-3}-3\right)\left(\sqrt{-3}+3\right)}$$

Ikkunsidra li \left(\sqrt{-3}-3\right)\left(\sqrt{-3}+3\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{-10\left(\sqrt{-3}+3\right)}{\left(\sqrt{-3}\right)^{2}-3^{2}}$$

Ikkwadra \sqrt{-3}. Ikkwadra 3.

$$\frac{-10\left(\sqrt{-3}+3\right)}{-3-9}$$

Naqqas 9 minn -3 biex tikseb -12.

$$\frac{-10\left(\sqrt{-3}+3\right)}{-12}$$

Iddividi -10\left(\sqrt{-3}+3\right) b'-12 biex tikseb\frac{5}{6}\left(\sqrt{-3}+3\right).

$$\frac{5}{6}\left(\sqrt{-3}+3\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{5}{6} b'\sqrt{-3}+3.

$$\frac{5}{6}\sqrt{-3}+\frac{5}{6}\times 3$$

Esprimi \frac{5}{6}\times 3 bħala frazzjoni waħda.

$$\frac{5}{6}\sqrt{-3}+\frac{5\times 3}{6}$$

Immultiplika 5 u 3 biex tikseb 15.

$$\frac{5}{6}\sqrt{-3}+\frac{15}{6}$$

Naqqas il-frazzjoni \frac{15}{6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{5}{6}\sqrt{-3}+\frac{5}{2}$$

Evalwa (complex solution)

$$\frac{5\sqrt{3}i}{6}+\frac{5}{2}\approx 2.5+1.443375673i$$

Parti Reali (complex solution)

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$