Lahenda 8(frac{5/sqrt{41})-3(4/sqrt{41})}{8(5/sqrt{41})+2(4/sqrt{41})}

$$\frac{ 8( \frac{ 5 }{ \sqrt{ 41 } } )-3( \frac{ 4 }{ \sqrt{ 41 } } ) }{ 8( \frac{ 5 }{ \sqrt{ 41 } } )+2( \frac{ 4 }{ \sqrt{ 41 } } ) }$$

Arvuta

$$\frac{7}{12}\approx 0,583333333$$

Lühike lahenduskäik

Vabastage \frac{5}{\sqrt{41}} nimetaja irratsionaalsusest, korrutades lugeja ja nimetaja arvuga \sqrt{41}.

$$\frac{8\times \frac{5\sqrt{41}}{\left(\sqrt{41}\right)^{2}}-3\times \frac{4}{\sqrt{41}}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

\sqrt{41} ruut on 41.

$$\frac{8\times \frac{5\sqrt{41}}{41}-3\times \frac{4}{\sqrt{41}}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Avaldage 8\times \frac{5\sqrt{41}}{41} ühe murdarvuna.

$$\frac{\frac{8\times 5\sqrt{41}}{41}-3\times \frac{4}{\sqrt{41}}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Vabastage \frac{4}{\sqrt{41}} nimetaja irratsionaalsusest, korrutades lugeja ja nimetaja arvuga \sqrt{41}.

$$\frac{\frac{8\times 5\sqrt{41}}{41}-3\times \frac{4\sqrt{41}}{\left(\sqrt{41}\right)^{2}}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

\sqrt{41} ruut on 41.

$$\frac{\frac{8\times 5\sqrt{41}}{41}-3\times \frac{4\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Avaldage 3\times \frac{4\sqrt{41}}{41} ühe murdarvuna.

$$\frac{\frac{8\times 5\sqrt{41}}{41}-\frac{3\times 4\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Korrutage 3 ja 4, et leida 12.

$$\frac{\frac{8\times 5\sqrt{41}}{41}-\frac{12\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Kuna murdudel \frac{8\times 5\sqrt{41}}{41} ja \frac{12\sqrt{41}}{41} on sama nimetaja, lahutage nende lugejad.

$$\frac{\frac{8\times 5\sqrt{41}-12\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Tehke korrutustehted võrrandis 8\times 5\sqrt{41}-12\sqrt{41}.

$$\frac{\frac{40\sqrt{41}-12\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Tehke arvutustehted avaldises 40\sqrt{41}-12\sqrt{41}.

$$\frac{\frac{28\sqrt{41}}{41}}{8\times \frac{5}{\sqrt{41}}+2\times \frac{4}{\sqrt{41}}}$$

Vabastage \frac{5}{\sqrt{41}} nimetaja irratsionaalsusest, korrutades lugeja ja nimetaja arvuga \sqrt{41}.

$$\frac{\frac{28\sqrt{41}}{41}}{8\times \frac{5\sqrt{41}}{\left(\sqrt{41}\right)^{2}}+2\times \frac{4}{\sqrt{41}}}$$

\sqrt{41} ruut on 41.

$$\frac{\frac{28\sqrt{41}}{41}}{8\times \frac{5\sqrt{41}}{41}+2\times \frac{4}{\sqrt{41}}}$$

Avaldage 8\times \frac{5\sqrt{41}}{41} ühe murdarvuna.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{8\times 5\sqrt{41}}{41}+2\times \frac{4}{\sqrt{41}}}$$

Vabastage \frac{4}{\sqrt{41}} nimetaja irratsionaalsusest, korrutades lugeja ja nimetaja arvuga \sqrt{41}.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{8\times 5\sqrt{41}}{41}+2\times \frac{4\sqrt{41}}{\left(\sqrt{41}\right)^{2}}}$$

\sqrt{41} ruut on 41.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{8\times 5\sqrt{41}}{41}+2\times \frac{4\sqrt{41}}{41}}$$

Avaldage 2\times \frac{4\sqrt{41}}{41} ühe murdarvuna.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{8\times 5\sqrt{41}}{41}+\frac{2\times 4\sqrt{41}}{41}}$$

Kuna murdudel \frac{8\times 5\sqrt{41}}{41} ja \frac{2\times 4\sqrt{41}}{41} on sama nimetaja, liitke nende lugejad.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{8\times 5\sqrt{41}+2\times 4\sqrt{41}}{41}}$$

Tehke korrutustehted võrrandis 8\times 5\sqrt{41}+2\times 4\sqrt{41}.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{40\sqrt{41}+8\sqrt{41}}{41}}$$

Tehke arvutustehted avaldises 40\sqrt{41}+8\sqrt{41}.

$$\frac{\frac{28\sqrt{41}}{41}}{\frac{48\sqrt{41}}{41}}$$

Jagage \frac{28\sqrt{41}}{41} väärtusega \frac{48\sqrt{41}}{41}, korrutades \frac{28\sqrt{41}}{41} väärtuse \frac{48\sqrt{41}}{41} pöördväärtusega.

$$\frac{28\sqrt{41}\times 41}{41\times 48\sqrt{41}}$$

Taandage 4\times 41\sqrt{41} nii lugejas kui ka nimetajas.

$$\frac{7}{12}$$

Lahuta teguriteks

$$\frac{7}{2 ^ {2} \cdot 3} = 0,5833333333333334$$