Solve f(x)=-28/4a-2/14+42/6/7

$$f ( x ) = \frac { \frac { - 28 } { 4 a } - \frac { 2 } { 14 } + \frac { 42 } { 6 } } { 7 }$$

Evaluate

$$\frac{48}{49}-\frac{1}{a}$$

Short Solution Steps

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+\frac{42}{6}}{7}$$

Divide 42 by 6 to get 7.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+7}{7}$$

Convert 7 to fraction \frac{49}{7}.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+\frac{49}{7}}{7}$$

Since -\frac{1}{7} and \frac{49}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28}{4a}+\frac{-1+49}{7}}{7}$$

Add -1 and 49 to get 48.

$$\frac{\frac{-28}{4a}+\frac{48}{7}}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a and 7 is 28a. Multiply \frac{-28}{4a} times \frac{7}{7}. Multiply \frac{48}{7} times \frac{4a}{4a}.

$$\frac{\frac{-28\times 7}{28a}+\frac{48\times 4a}{28a}}{7}$$

Since \frac{-28\times 7}{28a} and \frac{48\times 4a}{28a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28\times 7+48\times 4a}{28a}}{7}$$

Do the multiplications in -28\times 7+48\times 4a.

$$\frac{\frac{-196+192a}{28a}}{7}$$

Factor the expressions that are not already factored in \frac{-196+192a}{28a}.

$$\frac{\frac{4\left(48a-49\right)}{28a}}{7}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{48a-49}{7a}}{7}$$

Express \frac{\frac{48a-49}{7a}}{7} as a single fraction.

$$\frac{48a-49}{7a\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{48a-49}{49a}$$

Expand

$$\frac{48}{49}-\frac{1}{a}$$

Short Solution Steps

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+\frac{42}{6}}{7}$$

Divide 42 by 6 to get 7.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+7}{7}$$

Convert 7 to fraction \frac{49}{7}.

$$\frac{\frac{-28}{4a}-\frac{1}{7}+\frac{49}{7}}{7}$$

Since -\frac{1}{7} and \frac{49}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28}{4a}+\frac{-1+49}{7}}{7}$$

Add -1 and 49 to get 48.

$$\frac{\frac{-28}{4a}+\frac{48}{7}}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a and 7 is 28a. Multiply \frac{-28}{4a} times \frac{7}{7}. Multiply \frac{48}{7} times \frac{4a}{4a}.

$$\frac{\frac{-28\times 7}{28a}+\frac{48\times 4a}{28a}}{7}$$

Since \frac{-28\times 7}{28a} and \frac{48\times 4a}{28a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28\times 7+48\times 4a}{28a}}{7}$$

Do the multiplications in -28\times 7+48\times 4a.

$$\frac{\frac{-196+192a}{28a}}{7}$$

Factor the expressions that are not already factored in \frac{-196+192a}{28a}.

$$\frac{\frac{4\left(48a-49\right)}{28a}}{7}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{48a-49}{7a}}{7}$$

Express \frac{\frac{48a-49}{7a}}{7} as a single fraction.

$$\frac{48a-49}{7a\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{48a-49}{49a}$$