Solve 3/7-x/y7/9y/z3z

$$\frac{ 3 }{ 7 } - \frac{ x }{ y } \frac{ 7 }{ 9 } \frac{ y }{ z } 3z$$

Evaluate

$$-\frac{7x}{3}+\frac{3}{7}$$

Short Solution Steps

Express \frac{7}{9}\times 3 as a single fraction.

$$\frac{3}{7}-\frac{x}{y}\times \frac{7\times 3}{9}\times \frac{y}{z}z$$

Multiply 7 and 3 to get 21.

$$\frac{3}{7}-\frac{x}{y}\times \frac{21}{9}\times \frac{y}{z}z$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$\frac{3}{7}-\frac{x}{y}\times \frac{7}{3}\times \frac{y}{z}z$$

Multiply \frac{x}{y} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{7}-\frac{x\times 7}{y\times 3}\times \frac{y}{z}z$$

Multiply \frac{x\times 7}{y\times 3} times \frac{y}{z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{7}-\frac{x\times 7y}{y\times 3z}z$$

Cancel out y in both numerator and denominator.

$$\frac{3}{7}-\frac{7x}{3z}z$$

Express \frac{7x}{3z}z as a single fraction.

$$\frac{3}{7}-\frac{7xz}{3z}$$

Cancel out z in both numerator and denominator.

$$\frac{3}{7}-\frac{7x}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 3 is 21. Multiply \frac{3}{7} times \frac{3}{3}. Multiply \frac{7x}{3} times \frac{7}{7}.

$$\frac{3\times 3}{21}-\frac{7\times 7x}{21}$$

Since \frac{3\times 3}{21} and \frac{7\times 7x}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3-7\times 7x}{21}$$

Do the multiplications in 3\times 3-7\times 7x.

$$\frac{9-49x}{21}$$

Factor

$$\frac{9-49x}{21}$$