Solve y/y-11-y+6/7y-77+6/y

$$\frac { y } { y - 11 } - \frac { y + 6 } { 7 y - 77 } + \frac { 6 } { y }$$

Evaluate

$$\frac{6\left(y^{2}+6y-77\right)}{7y\left(y-11\right)}$$

Short Solution Steps

Factor 7y-77.

$$\frac{y}{y-11}-\frac{y+6}{7\left(y-11\right)}+\frac{6}{y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-11 and 7\left(y-11\right) is 7\left(y-11\right). Multiply \frac{y}{y-11} times \frac{7}{7}.

$$\frac{7y}{7\left(y-11\right)}-\frac{y+6}{7\left(y-11\right)}+\frac{6}{y}$$

Since \frac{7y}{7\left(y-11\right)} and \frac{y+6}{7\left(y-11\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7y-\left(y+6\right)}{7\left(y-11\right)}+\frac{6}{y}$$

Do the multiplications in 7y-\left(y+6\right).

$$\frac{7y-y-6}{7\left(y-11\right)}+\frac{6}{y}$$

Combine like terms in 7y-y-6.

$$\frac{6y-6}{7\left(y-11\right)}+\frac{6}{y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(y-11\right) and y is 7y\left(y-11\right). Multiply \frac{6y-6}{7\left(y-11\right)} times \frac{y}{y}. Multiply \frac{6}{y} times \frac{7\left(y-11\right)}{7\left(y-11\right)}.

$$\frac{\left(6y-6\right)y}{7y\left(y-11\right)}+\frac{6\times 7\left(y-11\right)}{7y\left(y-11\right)}$$

Since \frac{\left(6y-6\right)y}{7y\left(y-11\right)} and \frac{6\times 7\left(y-11\right)}{7y\left(y-11\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(6y-6\right)y+6\times 7\left(y-11\right)}{7y\left(y-11\right)}$$

Do the multiplications in \left(6y-6\right)y+6\times 7\left(y-11\right).

$$\frac{6y^{2}-6y+42y-462}{7y\left(y-11\right)}$$

Combine like terms in 6y^{2}-6y+42y-462.

$$\frac{6y^{2}+36y-462}{7y\left(y-11\right)}$$

Expand 7y\left(y-11\right).

$$\frac{6y^{2}+36y-462}{7y^{2}-77y}$$

Expand

$$\frac{6\left(y^{2}+6y-77\right)}{7y\left(y-11\right)}$$

Short Solution Steps

Factor 7y-77.

$$\frac{y}{y-11}-\frac{y+6}{7\left(y-11\right)}+\frac{6}{y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-11 and 7\left(y-11\right) is 7\left(y-11\right). Multiply \frac{y}{y-11} times \frac{7}{7}.

$$\frac{7y}{7\left(y-11\right)}-\frac{y+6}{7\left(y-11\right)}+\frac{6}{y}$$

Since \frac{7y}{7\left(y-11\right)} and \frac{y+6}{7\left(y-11\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7y-\left(y+6\right)}{7\left(y-11\right)}+\frac{6}{y}$$

Do the multiplications in 7y-\left(y+6\right).

$$\frac{7y-y-6}{7\left(y-11\right)}+\frac{6}{y}$$

Combine like terms in 7y-y-6.

$$\frac{6y-6}{7\left(y-11\right)}+\frac{6}{y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(y-11\right) and y is 7y\left(y-11\right). Multiply \frac{6y-6}{7\left(y-11\right)} times \frac{y}{y}. Multiply \frac{6}{y} times \frac{7\left(y-11\right)}{7\left(y-11\right)}.

$$\frac{\left(6y-6\right)y}{7y\left(y-11\right)}+\frac{6\times 7\left(y-11\right)}{7y\left(y-11\right)}$$

Since \frac{\left(6y-6\right)y}{7y\left(y-11\right)} and \frac{6\times 7\left(y-11\right)}{7y\left(y-11\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(6y-6\right)y+6\times 7\left(y-11\right)}{7y\left(y-11\right)}$$

Do the multiplications in \left(6y-6\right)y+6\times 7\left(y-11\right).

$$\frac{6y^{2}-6y+42y-462}{7y\left(y-11\right)}$$

Combine like terms in 6y^{2}-6y+42y-462.

$$\frac{6y^{2}+36y-462}{7y\left(y-11\right)}$$

Expand 7y\left(y-11\right).

$$\frac{6y^{2}+36y-462}{7y^{2}-77y}$$