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

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

Evaluate

$$\frac{\left(7x-1\right)\left(x+1\right)}{7x\left(x+2\right)}$$

Short Solution Steps

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

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

Since \frac{7x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x+1}{x+1}.

$$\frac{\frac{7x-1}{x}}{\frac{7\left(x+1\right)}{x+1}+\frac{7}{x+1}}$$

Since \frac{7\left(x+1\right)}{x+1} and \frac{7}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x-1}{x}}{\frac{7\left(x+1\right)+7}{x+1}}$$

Do the multiplications in 7\left(x+1\right)+7.

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

Combine like terms in 7x+7+7.

$$\frac{\frac{7x-1}{x}}{\frac{7x+14}{x+1}}$$

Divide \frac{7x-1}{x} by \frac{7x+14}{x+1} by multiplying \frac{7x-1}{x} by the reciprocal of \frac{7x+14}{x+1}.

$$\frac{\left(7x-1\right)\left(x+1\right)}{x\left(7x+14\right)}$$

Apply the distributive property by multiplying each term of 7x-1 by each term of x+1.

$$\frac{7x^{2}+7x-x-1}{x\left(7x+14\right)}$$

Combine 7x and -x to get 6x.

$$\frac{7x^{2}+6x-1}{x\left(7x+14\right)}$$

Use the distributive property to multiply x by 7x+14.

$$\frac{7x^{2}+6x-1}{7x^{2}+14x}$$

Expand

$$\frac{7x^{2}+6x-1}{7x\left(x+2\right)}$$

Short Solution Steps

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

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

Since \frac{7x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x+1}{x+1}.

$$\frac{\frac{7x-1}{x}}{\frac{7\left(x+1\right)}{x+1}+\frac{7}{x+1}}$$

Since \frac{7\left(x+1\right)}{x+1} and \frac{7}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x-1}{x}}{\frac{7\left(x+1\right)+7}{x+1}}$$

Do the multiplications in 7\left(x+1\right)+7.

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

Combine like terms in 7x+7+7.

$$\frac{\frac{7x-1}{x}}{\frac{7x+14}{x+1}}$$

Divide \frac{7x-1}{x} by \frac{7x+14}{x+1} by multiplying \frac{7x-1}{x} by the reciprocal of \frac{7x+14}{x+1}.

$$\frac{\left(7x-1\right)\left(x+1\right)}{x\left(7x+14\right)}$$

Apply the distributive property by multiplying each term of 7x-1 by each term of x+1.

$$\frac{7x^{2}+7x-x-1}{x\left(7x+14\right)}$$

Combine 7x and -x to get 6x.

$$\frac{7x^{2}+6x-1}{x\left(7x+14\right)}$$

Use the distributive property to multiply x by 7x+14.

$$\frac{7x^{2}+6x-1}{7x^{2}+14x}$$