Solve 1/3+1/2-lambda/6+2

$$\frac { 1 } { 3 } + \frac { 1 } { 2 } - \frac { \lambda } { 6 } + 2$$

Evaluate

$$\frac{17-\lambda }{6}$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{2}{6}+\frac{3}{6}-\frac{\lambda }{6}+2$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{6}-\frac{\lambda }{6}+2$$

Add 2 and 3 to get 5.

$$\frac{5}{6}-\frac{\lambda }{6}+2$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{5}{6}-\frac{\lambda }{6}+\frac{12}{6}$$

Since \frac{5}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{6}-\frac{\lambda }{6}$$

Add 5 and 12 to get 17.

$$\frac{17}{6}-\frac{\lambda }{6}$$

Since \frac{17}{6} and \frac{\lambda }{6} have the same denominator, add them by adding their numerators.

$$\frac{17+\lambda }{6}$$

Factor

$$\frac{17-\lambda }{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{17-\lambda }{6}$$

Consider 2+3-\lambda +12. Multiply and combine like terms.

$$-\lambda +17$$

Rewrite the complete factored expression.

$$\frac{-\lambda +17}{6}$$