Solve 5/x+1/3-frac{x{7}}

$$\frac { \frac { 5 } { x } + 1 } { 3 - \frac { x } { 7 } }$$

Evaluate

$$\frac{7\left(x+5\right)}{x\left(21-x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{5}{x}+\frac{x}{x}}{3-\frac{x}{7}}$$

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

$$\frac{\frac{5+x}{x}}{3-\frac{x}{7}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{7}{7}.

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

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

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

Do the multiplications in 3\times 7-x.

$$\frac{\frac{5+x}{x}}{\frac{21-x}{7}}$$

Divide \frac{5+x}{x} by \frac{21-x}{7} by multiplying \frac{5+x}{x} by the reciprocal of \frac{21-x}{7}.

$$\frac{\left(5+x\right)\times 7}{x\left(21-x\right)}$$

Use the distributive property to multiply 5+x by 7.

$$\frac{35+7x}{x\left(21-x\right)}$$

Use the distributive property to multiply x by 21-x.

$$\frac{35+7x}{21x-x^{2}}$$

Expand

$$-\frac{7\left(x+5\right)}{x\left(x-21\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{5}{x}+\frac{x}{x}}{3-\frac{x}{7}}$$

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

$$\frac{\frac{5+x}{x}}{3-\frac{x}{7}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{7}{7}.

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

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

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

Do the multiplications in 3\times 7-x.

$$\frac{\frac{5+x}{x}}{\frac{21-x}{7}}$$

Divide \frac{5+x}{x} by \frac{21-x}{7} by multiplying \frac{5+x}{x} by the reciprocal of \frac{21-x}{7}.

$$\frac{\left(5+x\right)\times 7}{x\left(21-x\right)}$$

Use the distributive property to multiply 5+x by 7.

$$\frac{35+7x}{x\left(21-x\right)}$$

Use the distributive property to multiply x by 21-x.

$$\frac{35+7x}{21x-x^{2}}$$