Solve 6y-z/2y-2z-z-8y/4y-4z

$$\frac { 6 y - z } { 2 y - 2 z } - \frac { z - 8 y } { 4 y - 4 z }$$

Evaluate

$$\frac{20y-3z}{4\left(y-z\right)}$$

Short Solution Steps

Factor 2y-2z. Factor 4y-4z.

$$\frac{6y-z}{2\left(y-z\right)}-\frac{z-8y}{4\left(y-z\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(y-z\right) and 4\left(y-z\right) is 4\left(y-z\right). Multiply \frac{6y-z}{2\left(y-z\right)} times \frac{2}{2}.

$$\frac{2\left(6y-z\right)}{4\left(y-z\right)}-\frac{z-8y}{4\left(y-z\right)}$$

Since \frac{2\left(6y-z\right)}{4\left(y-z\right)} and \frac{z-8y}{4\left(y-z\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(6y-z\right)-\left(z-8y\right)}{4\left(y-z\right)}$$

Do the multiplications in 2\left(6y-z\right)-\left(z-8y\right).

$$\frac{12y-2z-z+8y}{4\left(y-z\right)}$$

Combine like terms in 12y-2z-z+8y.

$$\frac{20y-3z}{4\left(y-z\right)}$$

Expand 4\left(y-z\right).

$$\frac{20y-3z}{4y-4z}$$

Expand

$$\frac{3z-20y}{4\left(z-y\right)}$$

Short Solution Steps

Factor 2y-2z. Factor 4y-4z.

$$\frac{6y-z}{2\left(y-z\right)}-\frac{z-8y}{4\left(y-z\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(y-z\right) and 4\left(y-z\right) is 4\left(y-z\right). Multiply \frac{6y-z}{2\left(y-z\right)} times \frac{2}{2}.

$$\frac{2\left(6y-z\right)}{4\left(y-z\right)}-\frac{z-8y}{4\left(y-z\right)}$$

Since \frac{2\left(6y-z\right)}{4\left(y-z\right)} and \frac{z-8y}{4\left(y-z\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(6y-z\right)-\left(z-8y\right)}{4\left(y-z\right)}$$

Do the multiplications in 2\left(6y-z\right)-\left(z-8y\right).

$$\frac{12y-2z-z+8y}{4\left(y-z\right)}$$

Combine like terms in 12y-2z-z+8y.

$$\frac{20y-3z}{4\left(y-z\right)}$$

Expand 4\left(y-z\right).

$$\frac{20y-3z}{4y-4z}$$