Solve 5(1/x)+3/6(frac{1{x})+7}

$$\frac { 5 ( \frac { 1 } { x } ) + 3 } { 6 ( \frac { 1 } { x } ) + 7 }$$

Evaluate

$$\frac{3x+5}{7x+6}$$

Solution Steps

Express 5\times \frac{1}{x} as a single fraction.

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

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

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

Since \frac{5}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

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

Express 6\times \frac{1}{x} as a single fraction.

$$\frac{\frac{5+3x}{x}}{\frac{6}{x}+7}$$

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

$$\frac{\frac{5+3x}{x}}{\frac{6}{x}+\frac{7x}{x}}$$

Since \frac{6}{x} and \frac{7x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+3x}{x}}{\frac{6+7x}{x}}$$

Divide \frac{5+3x}{x} by \frac{6+7x}{x} by multiplying \frac{5+3x}{x} by the reciprocal of \frac{6+7x}{x}.

$$\frac{\left(5+3x\right)x}{x\left(6+7x\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3x+5}{7x+6}$$

Expand

$$\frac{3x+5}{7x+6}$$

Solution Steps

Express 5\times \frac{1}{x} as a single fraction.

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

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

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

Since \frac{5}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

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

Express 6\times \frac{1}{x} as a single fraction.

$$\frac{\frac{5+3x}{x}}{\frac{6}{x}+7}$$

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

$$\frac{\frac{5+3x}{x}}{\frac{6}{x}+\frac{7x}{x}}$$

Since \frac{6}{x} and \frac{7x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+3x}{x}}{\frac{6+7x}{x}}$$

Divide \frac{5+3x}{x} by \frac{6+7x}{x} by multiplying \frac{5+3x}{x} by the reciprocal of \frac{6+7x}{x}.

$$\frac{\left(5+3x\right)x}{x\left(6+7x\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3x+5}{7x+6}$$