Solve -2,4alpha/0,12-0,24/1,2+50omega/15-21omega/9+1+frac{38alpha}{57}+frac{65alpha}{26}+9omega

$$- \frac { 2,4 \alpha } { 0,12 } - \frac { 0,24 } { 1,2 } + \frac { 50 \omega } { 15 } - \frac { 21 \omega } { 9 } + 1 + \frac { 38 \alpha } { 57 } + \frac { 65 \alpha } { 26 } + 9 \omega$$

Evaluate

$$-\frac{101\alpha }{6}+10\omega +0,8$$

Solution Steps

Divide 2,4\alpha by 0,12 to get 20\alpha .

$$-20\alpha -\frac{0,24}{1,2}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Expand \frac{0,24}{1,2} by multiplying both numerator and the denominator by 100.

$$-20\alpha -\frac{24}{120}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Reduce the fraction \frac{24}{120} to lowest terms by extracting and canceling out 24.

$$-20\alpha -\frac{1}{5}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Divide 50\omega by 15 to get \frac{10}{3}\omega .

$$-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Divide 21\omega by 9 to get \frac{7}{3}\omega .

$$-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Convert 1 to fraction \frac{5}{5}.

$$-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{5}{5}+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Since -\frac{1}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$-20\alpha +\frac{-1+5}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Add -1 and 5 to get 4.

$$-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega$$

Divide 38\alpha by 57 to get \frac{2}{3}\alpha .

$$-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{2}{3}\alpha +\frac{65\alpha }{26}+9\omega$$

Divide 65\alpha by 26 to get \frac{5}{2}\alpha .

$$-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{2}{3}\alpha +\frac{5}{2}\alpha +9\omega$$

Combine \frac{2}{3}\alpha and \frac{5}{2}\alpha to get \frac{19}{6}\alpha .

$$-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{19}{6}\alpha +9\omega$$

Combine \frac{10}{3}\omega and 9\omega to get \frac{37}{3}\omega .

$$-20\alpha +\frac{4}{5}+\frac{37}{3}\omega -\frac{7}{3}\omega +\frac{19}{6}\alpha$$

Combine \frac{37}{3}\omega and -\frac{7}{3}\omega to get 10\omega .

$$-20\alpha +\frac{4}{5}+10\omega +\frac{19}{6}\alpha$$

Combine -20\alpha and \frac{19}{6}\alpha to get -\frac{101}{6}\alpha .

$$-\frac{101}{6}\alpha +\frac{4}{5}+10\omega$$

Factor

$$\frac{4,8+60\omega -101\alpha }{6}$$

Solution Steps

Divide 2,4\alpha by 0,12 to get 20\alpha .

$$factor(-20\alpha -\frac{0,24}{1,2}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Expand \frac{0,24}{1,2} by multiplying both numerator and the denominator by 100.

$$factor(-20\alpha -\frac{24}{120}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Reduce the fraction \frac{24}{120} to lowest terms by extracting and canceling out 24.

$$factor(-20\alpha -\frac{1}{5}+\frac{50\omega }{15}-\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Divide 50\omega by 15 to get \frac{10}{3}\omega .

$$factor(-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{21\omega }{9}+1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Divide 21\omega by 9 to get \frac{7}{3}\omega .

$$factor(-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +1+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Convert 1 to fraction \frac{5}{5}.

$$factor(-20\alpha -\frac{1}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{5}{5}+\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Since -\frac{1}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$factor(-20\alpha +\frac{-1+5}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Add -1 and 5 to get 4.

$$factor(-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{38\alpha }{57}+\frac{65\alpha }{26}+9\omega )$$

Divide 38\alpha by 57 to get \frac{2}{3}\alpha .

$$factor(-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{2}{3}\alpha +\frac{65\alpha }{26}+9\omega )$$

Divide 65\alpha by 26 to get \frac{5}{2}\alpha .

$$factor(-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{2}{3}\alpha +\frac{5}{2}\alpha +9\omega )$$

Combine \frac{2}{3}\alpha and \frac{5}{2}\alpha to get \frac{19}{6}\alpha .

$$factor(-20\alpha +\frac{4}{5}+\frac{10}{3}\omega -\frac{7}{3}\omega +\frac{19}{6}\alpha +9\omega )$$

Combine \frac{10}{3}\omega and 9\omega to get \frac{37}{3}\omega .

$$factor(-20\alpha +\frac{4}{5}+\frac{37}{3}\omega -\frac{7}{3}\omega +\frac{19}{6}\alpha )$$

Combine \frac{37}{3}\omega and -\frac{7}{3}\omega to get 10\omega .

$$factor(-20\alpha +\frac{4}{5}+10\omega +\frac{19}{6}\alpha )$$

Combine -20\alpha and \frac{19}{6}\alpha to get -\frac{101}{6}\alpha .

$$factor(-\frac{101}{6}\alpha +\frac{4}{5}+10\omega )$$

Factor out \frac{1}{30}.

$$\frac{-505\alpha +24+300\omega }{30}$$