Issolvi frac{frac{sqrt{3}}{2}-154/308^2}{frac{sqrt{3}}{2}+154/308^2}

$$\frac{ \frac{ \sqrt{ 3 } }{ 2 } - \frac{ 154 }{ { 308 }^{ 2 } } }{ \frac{ \sqrt{ 3 } }{ 2 } + \frac{ 154 }{ { 308 }^{ 2 } } }$$

Evalwa

$$\frac{284593-616\sqrt{3}}{284591}\approx 0.996257987$$

Passi Qosra tas-Soluzzjonijiet

Ikkalkula 308 bil-power ta' 2 u tikseb 94864.

$$\frac{\frac{\sqrt{3}}{2}-\frac{154}{94864}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Naqqas il-frazzjoni \frac{154}{94864} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 154.

$$\frac{\frac{\sqrt{3}}{2}-\frac{1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 2 u 616 huwa 616. Immultiplika \frac{\sqrt{3}}{2} b'\frac{308}{308}.

$$\frac{\frac{308\sqrt{3}}{616}-\frac{1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Billi \frac{308\sqrt{3}}{616} u \frac{1}{616} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{308^{2}}}$$

Ikkalkula 308 bil-power ta' 2 u tikseb 94864.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{154}{94864}}$$

Naqqas il-frazzjoni \frac{154}{94864} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 154.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{\sqrt{3}}{2}+\frac{1}{616}}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 2 u 616 huwa 616. Immultiplika \frac{\sqrt{3}}{2} b'\frac{308}{308}.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{308\sqrt{3}}{616}+\frac{1}{616}}$$

Billi \frac{308\sqrt{3}}{616} u \frac{1}{616} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\frac{308\sqrt{3}-1}{616}}{\frac{308\sqrt{3}+1}{616}}$$

Iddividi \frac{308\sqrt{3}-1}{616} b'\frac{308\sqrt{3}+1}{616} billi timmultiplika \frac{308\sqrt{3}-1}{616} bir-reċiproku ta' \frac{308\sqrt{3}+1}{616}.

$$\frac{\left(308\sqrt{3}-1\right)\times 616}{616\left(308\sqrt{3}+1\right)}$$

Annulla 616 fin-numeratur u d-denominatur.

$$\frac{308\sqrt{3}-1}{308\sqrt{3}+1}$$

Irrazzjonalizza d-denominatur tal-\frac{308\sqrt{3}-1}{308\sqrt{3}+1} billi timmultiplika in-numeratur u d-denominatur mill-308\sqrt{3}-1.

$$\frac{\left(308\sqrt{3}-1\right)\left(308\sqrt{3}-1\right)}{\left(308\sqrt{3}+1\right)\left(308\sqrt{3}-1\right)}$$

Ikkunsidra li \left(308\sqrt{3}+1\right)\left(308\sqrt{3}-1\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}.

$$\frac{\left(308\sqrt{3}-1\right)\left(308\sqrt{3}-1\right)}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Immultiplika 308\sqrt{3}-1 u 308\sqrt{3}-1 biex tikseb \left(308\sqrt{3}-1\right)^{2}.

$$\frac{\left(308\sqrt{3}-1\right)^{2}}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(308\sqrt{3}-1\right)^{2}.

$$\frac{94864\left(\sqrt{3}\right)^{2}-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{94864\times 3-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Immultiplika 94864 u 3 biex tikseb 284592.

$$\frac{284592-616\sqrt{3}+1}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Żid 284592 u 1 biex tikseb 284593.

$$\frac{284593-616\sqrt{3}}{\left(308\sqrt{3}\right)^{2}-1^{2}}$$

Espandi \left(308\sqrt{3}\right)^{2}.

$$\frac{284593-616\sqrt{3}}{308^{2}\left(\sqrt{3}\right)^{2}-1^{2}}$$

Ikkalkula 308 bil-power ta' 2 u tikseb 94864.

$$\frac{284593-616\sqrt{3}}{94864\left(\sqrt{3}\right)^{2}-1^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{284593-616\sqrt{3}}{94864\times 3-1^{2}}$$

Immultiplika 94864 u 3 biex tikseb 284592.

$$\frac{284593-616\sqrt{3}}{284592-1^{2}}$$

Ikkalkula 1 bil-power ta' 2 u tikseb 1.

$$\frac{284593-616\sqrt{3}}{284592-1}$$

Naqqas 1 minn 284592 biex tikseb 284591.

$$\frac{284593-616\sqrt{3}}{284591}$$

Fattur

$$\frac{284593 - 616 \sqrt{3}}{284591} = 0.9962579867337251$$