Solve 3+4/2*3*4-9/4*5*6+4/6*7*x

$$3 + \frac { 4 } { 2 \times 3 \times 4 } - \frac { 9 } { 4 \times 5 \times 6 } + \frac { 4 } { 6 \times 7 \times x }$$

Evaluate

$$\frac{371}{120}+\frac{2}{21x}$$

Short Solution Steps

Multiply 2 and 3 to get 6.

$$3+\frac{4}{6\times 4}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Multiply 6 and 4 to get 24.

$$3+\frac{4}{24}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

$$3+\frac{1}{6}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{18}{6}+\frac{1}{6}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Since \frac{18}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{18+1}{6}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Add 18 and 1 to get 19.

$$\frac{19}{6}-\frac{9}{4\times 5\times 6}+\frac{4}{6\times 7x}$$

Multiply 4 and 5 to get 20.

$$\frac{19}{6}-\frac{9}{20\times 6}+\frac{4}{6\times 7x}$$

Multiply 20 and 6 to get 120.

$$\frac{19}{6}-\frac{9}{120}+\frac{4}{6\times 7x}$$

Reduce the fraction \frac{9}{120} to lowest terms by extracting and canceling out 3.

$$\frac{19}{6}-\frac{3}{40}+\frac{4}{6\times 7x}$$

Least common multiple of 6 and 40 is 120. Convert \frac{19}{6} and \frac{3}{40} to fractions with denominator 120.

$$\frac{380}{120}-\frac{9}{120}+\frac{4}{6\times 7x}$$

Since \frac{380}{120} and \frac{9}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{380-9}{120}+\frac{4}{6\times 7x}$$

Subtract 9 from 380 to get 371.

$$\frac{371}{120}+\frac{4}{6\times 7x}$$

Multiply 6 and 7 to get 42.

$$\frac{371}{120}+\frac{4}{42x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 120 and 42x is 840x. Multiply \frac{371}{120} times \frac{7x}{7x}. Multiply \frac{4}{42x} times \frac{20}{20}.

$$\frac{371\times 7x}{840x}+\frac{4\times 20}{840x}$$

Since \frac{371\times 7x}{840x} and \frac{4\times 20}{840x} have the same denominator, add them by adding their numerators.

$$\frac{371\times 7x+4\times 20}{840x}$$

Do the multiplications in 371\times 7x+4\times 20.

$$\frac{2597x+80}{840x}$$

Factor

$$\frac{2597x+80}{840x}$$