Solve (2/3+3/4+2)*1/a+3

$$( \frac { 2 } { 3 } + \frac { 3 } { 4 } + 2 ) \cdot \frac { 1 } { a + 3 }$$

Evaluate

$$\frac{41}{12\left(a+3\right)}$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\left(\frac{8}{12}+\frac{9}{12}+2\right)\times \frac{1}{a+3}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\left(\frac{8+9}{12}+2\right)\times \frac{1}{a+3}$$

Add 8 and 9 to get 17.

$$\left(\frac{17}{12}+2\right)\times \frac{1}{a+3}$$

Convert 2 to fraction \frac{24}{12}.

$$\left(\frac{17}{12}+\frac{24}{12}\right)\times \frac{1}{a+3}$$

Since \frac{17}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{17+24}{12}\times \frac{1}{a+3}$$

Add 17 and 24 to get 41.

$$\frac{41}{12}\times \frac{1}{a+3}$$

Multiply \frac{41}{12} times \frac{1}{a+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{12\left(a+3\right)}$$

Use the distributive property to multiply 12 by a+3.

$$\frac{41}{12a+36}$$

Expand

$$\frac{41}{12\left(a+3\right)}$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\left(\frac{8}{12}+\frac{9}{12}+2\right)\times \frac{1}{a+3}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\left(\frac{8+9}{12}+2\right)\times \frac{1}{a+3}$$

Add 8 and 9 to get 17.

$$\left(\frac{17}{12}+2\right)\times \frac{1}{a+3}$$

Convert 2 to fraction \frac{24}{12}.

$$\left(\frac{17}{12}+\frac{24}{12}\right)\times \frac{1}{a+3}$$

Since \frac{17}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{17+24}{12}\times \frac{1}{a+3}$$

Add 17 and 24 to get 41.

$$\frac{41}{12}\times \frac{1}{a+3}$$

Multiply \frac{41}{12} times \frac{1}{a+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{12\left(a+3\right)}$$

Use the distributive property to multiply 12 by a+3.

$$\frac{41}{12a+36}$$