Trigonometrie Beispiele

$\frac{x + 3}{40} + \frac{x - 5}{24} = \frac{x - 2}{15}$

Schritt 1

Vereinfache $\frac{x + 3}{40} + \frac{x - 5}{24}$ .

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Schritt 1.1

Um $\frac{x + 3}{40}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{3}{3}$ .

$\frac{x + 3}{40} \cdot \frac{3}{3} + \frac{x - 5}{24} = \frac{x - 2}{15}$

Schritt 1.2

Um $\frac{x - 5}{24}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{5}{5}$ .

$\frac{x + 3}{40} \cdot \frac{3}{3} + \frac{x - 5}{24} \cdot \frac{5}{5} = \frac{x - 2}{15}$

Schritt 1.3

Schreibe jeden Ausdruck mit einem gemeinsamen Nenner von $120$ , indem du jeden mit einem entsprechenden Faktor von $1$ multiplizierst.

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Schritt 1.3.1

Mutltipliziere $\frac{x + 3}{40}$ mit $\frac{3}{3}$ .

$\frac{(x + 3) \cdot 3}{40 \cdot 3} + \frac{x - 5}{24} \cdot \frac{5}{5} = \frac{x - 2}{15}$

Schritt 1.3.2

Mutltipliziere $40$ mit $3$ .

$\frac{(x + 3) \cdot 3}{120} + \frac{x - 5}{24} \cdot \frac{5}{5} = \frac{x - 2}{15}$

Schritt 1.3.3

Mutltipliziere $\frac{x - 5}{24}$ mit $\frac{5}{5}$ .

$\frac{(x + 3) \cdot 3}{120} + \frac{(x - 5) \cdot 5}{24 \cdot 5} = \frac{x - 2}{15}$

Schritt 1.3.4

Mutltipliziere $24$ mit $5$ .

$\frac{(x + 3) \cdot 3}{120} + \frac{(x - 5) \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.4

Vereinige die Zähler über dem gemeinsamen Nenner.

$\frac{(x + 3) \cdot 3 + (x - 5) \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5

Vereinfache den Zähler.

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Schritt 1.5.1

Wende das Distributivgesetz an.

$\frac{x \cdot 3 + 3 \cdot 3 + (x - 5) \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5.2

Bringe $3$ auf die linke Seite von $x$ .

$\frac{3 \cdot x + 3 \cdot 3 + (x - 5) \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5.3

Mutltipliziere $3$ mit $3$ .

$\frac{3 \cdot x + 9 + (x - 5) \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5.4

Wende das Distributivgesetz an.

$\frac{3 x + 9 + x \cdot 5 - 5 \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5.5

Bringe $5$ auf die linke Seite von $x$ .

$\frac{3 x + 9 + 5 \cdot x - 5 \cdot 5}{120} = \frac{x - 2}{15}$

Schritt 1.5.6

Mutltipliziere $- 5$ mit $5$ .

$\frac{3 x + 9 + 5 \cdot x - 25}{120} = \frac{x - 2}{15}$

Schritt 1.5.7

Addiere $3 x$ und $5 x$ .

$\frac{8 x + 9 - 25}{120} = \frac{x - 2}{15}$

Schritt 1.5.8

Subtrahiere $25$ von $9$ .

$\frac{8 x - 16}{120} = \frac{x - 2}{15}$

Schritt 1.5.9

Faktorisiere $8$ aus $8 x - 16$ heraus.

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Schritt 1.5.9.1

Faktorisiere $8$ aus $8 x$ heraus.

$\frac{8 (x) - 16}{120} = \frac{x - 2}{15}$

Schritt 1.5.9.2

Faktorisiere $8$ aus $- 16$ heraus.

$\frac{8 x + 8 \cdot - 2}{120} = \frac{x - 2}{15}$

Schritt 1.5.9.3

Faktorisiere $8$ aus $8 x + 8 \cdot - 2$ heraus.

$\frac{8 (x - 2)}{120} = \frac{x - 2}{15}$

Schritt 1.6

Kürze die gemeinsamen Faktoren.

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Schritt 1.6.1

Faktorisiere $8$ aus $120$ heraus.

$\frac{8 (x - 2)}{8 \cdot 15} = \frac{x - 2}{15}$

Schritt 1.6.2

Kürze den gemeinsamen Faktor.

$\frac{8 (x - 2)}{8 \cdot 15} = \frac{x - 2}{15}$

Schritt 1.6.3

Forme den Ausdruck um.

$\frac{x - 2}{15} = \frac{x - 2}{15}$

Schritt 2

Stelle jede Seite der Gleichung graphisch dar. Die Lösung ist der x-Wert des Schnittpunktes.

$x \approx - 50, - 49.9, - 49.4, - 49.3, - 49.1, - 49, - 48.9, - 48.8, - 48.7, - 48.6, - 48.5, - 48.4, - 47.9, - 47.8, - 47.6, - 47.5, - 47.4, - 47.3, - 47.2, - 47.1, - 47, - 46.9, - 46.3\overline{9}, - 46.2\overline{9}, - 46.0\overline{9}, - 46, - 45.8\overline{9}, - 45.7\overline{9}, - 45.6\overline{9}, - 45.5\overline{9}, - 45.4\overline{9}, - 45.3\overline{9}, - 44.8\overline{9}, - 44.7\overline{9}, - 44.5\overline{9}, - 44.4\overline{9}, - 44.3\overline{9}, - 44.1\overline{9}, - 44.0\overline{9}, - 44, - 43.8\overline{9}, - 43.3\overline{9}, - 43.2\overline{9}, - 43.0\overline{9}, - 43, - 42.7\overline{9}, - 42.6\overline{9}, - 42.5\overline{9}, - 42.4\overline{9}, - 41.7\overline{9}, - 41.6\overline{9}, - 41.0\overline{9}, - 41, - 40.2\overline{9}, - 40.1\overline{9}, - 39.7\overline{9}, - 39.6\overline{9}, - 39.5\overline{9}, - 39.4\overline{9}, - 39, - 38.8\overline{9}, - 38.7\overline{9}, - 38.6\overline{9}, - 38.2\overline{9}, - 38.1\overline{9}, - 38.0\overline{9}, - 38, - 37.2\overline{9}, - 37.1\overline{9}, - 36.7\overline{9}, - 36.6\overline{9}, - 36.5\overline{9}, - 36.4\overline{9}, - 35.7\overline{9}, - 35.6\overline{9}, - 35.2\overline{9}, - 35.1\overline{9}, - 35.0\overline{9}, - 35, - 34.2\overline{9}, - 34.1\overline{9}, - 33.7\overline{9}, - 33.6\overline{9}, - 33.5\overline{9}, - 33.4\overline{9}, - 32.7\overline{9}, - 32.6\overline{9}, - 32.2\overline{9}, - 32.1\overline{9}, - 32.0\overline{9}, - 31.8\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 30.7\overline{9}, - 30.6\overline{9}, - 30.4\overline{9}, - 29.6\overline{9}, - 29.5\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.2\overline{9}, - 29.1\overline{9}, - 28.6\overline{9}, - 28.5\overline{9}, - 28.2\overline{9}, - 28.1\overline{9}, - 28.0\overline{9}, - 28, - 27.8\overline{9}, - 27.7\overline{9}, - 27.6\overline{9}, - 27.5\overline{9}, - 27.4\overline{9}, - 27.3\overline{9}, - 27.0\overline{9}, - 27, - 26.8\overline{9}, - 26.7\overline{9}, - 26.4\overline{9}, - 26.3\overline{9}, - 26, - 25.8\overline{9}, - 25.5\overline{9}, - 25.4\overline{9}, - 25.3\overline{9}, - 25.2\overline{9}, - 25.0\overline{9}, - 25, - 24.6\overline{9}, - 24.5\overline{9}, - 24.4\overline{9}, - 24.3\overline{9}, - 24.0\overline{9}, - 24, - 23.8\overline{9}, - 23.7\overline{9}, - 23.6\overline{9}, - 23.5\overline{9}, - 23.3\overline{9}, - 23.2\overline{9}, - 23.1\overline{9}, - 23.0\overline{9}, - 23, - 22.8\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22, - 21.8\overline{9}, - 21.4\overline{9}, - 21.3\overline{9}, - 21.0\overline{9}, - 21, - 20.5\overline{9}, - 20.4\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 20, - 19.8\overline{9}, - 19.5\overline{9}, - 19.4\overline{9}, - 19.3\overline{9}, - 19.2\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18, - 17.8\overline{9}, - 17.7\overline{9}, - 17.6\overline{9}, - 17.2\overline{9}, - 17.1\overline{9}, - \frac{33}{2}, - 16.3\overline{9}, - 16.2\overline{9}, - 16.1\overline{9}, - 15.8\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - \frac{31}{2}, - 15.3\overline{9}, - 14.8\overline{9}, - 14.7\overline{9}, - \frac{29}{2}, - 14.3\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.3\overline{9}, - 13.2\overline{9}, - 13, - 12.8\overline{9}, - 12.6\overline{9}, - \frac{62}{5}, - 12.1\overline{9}, - 12.0\overline{9}, - 11.8\overline{9}, - \frac{59}{5}, - \frac{23}{2}, - \frac{57}{5}, - 11.2\overline{9}, - 11.0\overline{9}, - \frac{54}{5}, - \frac{53}{5}, - \frac{21}{2}, - 10.2\overline{9}, - 9.9, - \frac{49}{5}, - 9.7, - \frac{48}{5}, - \frac{47}{5}, - \frac{46}{5}, - 8.9, - 8.7, - \frac{42}{5}, - \frac{41}{5}, - \frac{39}{5}, - 7.7, - \frac{38}{5}, - \frac{15}{2}, - 7.3, - \frac{36}{5}, - 7.1, - 7, - 6.9, - \frac{13}{2}, - \frac{32}{5}, - 6, - 5.9, - \frac{26}{5}, - 5, - 4.7, - \frac{9}{2}, - \frac{21}{5}, - 4, - 3.9, - \frac{19}{5}, - \frac{7}{2}, - 3.1, - \frac{14}{5}, - 2.3, - \frac{11}{5}, - 2, - 1.9, - 1.7, - \frac{3}{2}, - \frac{7}{5}, - \frac{6}{5}, - 1.1, - 1, - \frac{4}{5}, - 0.7, - \frac{3}{5}, - \frac{1}{2}, - \frac{2}{5}, - 0.3, - \frac{1}{5}, - 0.1, 0, 0.1, \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}, 0.9, 1, 1.1, \frac{6}{5}, 1.3, \frac{7}{5}, \frac{3}{2}, \frac{8}{5}, 1.7, \frac{9}{5}, 1.9, 2, 2.3, \frac{12}{5}, 2.7, \frac{14}{5}, 3.1, \frac{16}{5}, \frac{17}{5}, \frac{7}{2}, \frac{18}{5}, 3.7, 3.9, 4, 4.1, 4.3, \frac{22}{5}, \frac{9}{2}, \frac{23}{5}, \frac{24}{5}, 4.9, 5, 5.1, 5.3, \frac{27}{5}, \frac{11}{2}, \frac{28}{5}, 6.1, 6.3, \frac{33}{5}, \frac{34}{5}, 7, \frac{37}{5}, \frac{15}{2}, 7.9, 8.1, \frac{41}{5}, \frac{42}{5}, \frac{17}{2}, \frac{43}{5}, 8.7, 8.9, 9, 9.1, \frac{46}{5}, 9.3, 9.9, 10, \frac{52}{5}, \frac{21}{2}, 10.9, 11, \frac{56}{5}, 11.3, \frac{57}{5}, \frac{23}{2}, 11.7, \frac{59}{5}, 11.9, 12, \frac{62}{5}, \frac{25}{2}, 12.6, 12.7, 12.8, 12.9, 13, 13.1, 13.2, 13.4, \frac{27}{2}, 13.7, 13.9, 14, 14.2, 14.4, \frac{29}{2}, 14.6, 14.8, 14.9, 15, 15.1, 15.3, 15.4, \frac{31}{2}, 15.7, 16.3, 16.4, 16.6, 16.7, 16.8, 16.9, 17.1, 17.2, \frac{35}{2}, 17.7, 17.8, 17.9, 18.4, 18.5, 18.6, 18.7, 19, 19.2, 19.3, 19.4, 19.7, 19.8, 20, 20.1, 20.2, 20.3, 20.4, 20.5, 20.6, 20.8, 20.9, 21.3, 21.4, 21.6, 21.7, 21.8, 22, 22.2, 22.3, 22.4, 22.9, 23, 23.1, 23.2, 23.5, 23.7, 23.8, 23.9, 24.2, 24.3, 24.5, 24.6, 24.7, 24.8, 24.9, 25, 25.2, 25.8, 26, 26.1, 26.2, 26.3, 26.5, 26.7, 26.8, 26.9, 27.4, 27.5, 27.6, 27.7, 28, 28.2, 28.3, 28.4, 28.7, 28.8, 29, 29.1, 29.2, 29.4, 29.5, 29.6, 29.9, 30, 30.2, 30.3, 30.5, 30.6, 30.7, 30.8, 31, 31.2, 31.3, 31.4, 31.9, 32, 32.4, 32.5, 32.9, 33, 33.1, 33.2, 33.9, 34, 34.4, 34.5, 34.6, 34.7, 35.4, 35.5, 35.9, 36, 36.1, 36.2, 36.9, 37, 37.4, 37.6, 37.8, 38.3, 38.4, 38.9, 39.1, 39.3, 39.8, 40, 40.4, 40.6, 40.8, 41.2, 41.3, 41.5, 41.9, 42.1, 42.3, 42.8, 43, 43.4, 43.6, 43.8, 44.3, 44.5, 44.9, 45.1, 45.3, 45.8, 46, 46.4, 46.6, 46.7, 46.8, 47.3, 47.4, 47.9, 48.1, 48.3, 48.8, 49, 49.4, 49.6, 49.8$

Schritt 3