Solve 3y-1/y(y-2)-3y-2/(-y+1)(-y+2)

$$\frac { 3 y - 1 } { y ( y - 2 ) } - \frac { 3 y - 2 } { ( - y + 1 ) ( - y + 2 ) }$$

Evaluate

$$\frac{2y-1}{y\left(1-y\right)\left(y-2\right)}$$

Short Solution Steps

Factor \left(-y+1\right)\left(-y+2\right).

$$\frac{3y-1}{y\left(y-2\right)}-\frac{3y-2}{\left(-y+1\right)\left(-y+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(y-2\right) and \left(-y+1\right)\left(-y+2\right) is y\left(y-2\right)\left(y-1\right). Multiply \frac{3y-1}{y\left(y-2\right)} times \frac{y-1}{y-1}. Multiply \frac{3y-2}{\left(-y+1\right)\left(-y+2\right)} times \frac{y}{y}.

$$\frac{\left(3y-1\right)\left(y-1\right)}{y\left(y-2\right)\left(y-1\right)}-\frac{\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)}$$

Since \frac{\left(3y-1\right)\left(y-1\right)}{y\left(y-2\right)\left(y-1\right)} and \frac{\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3y-1\right)\left(y-1\right)-\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)}$$

Do the multiplications in \left(3y-1\right)\left(y-1\right)-\left(3y-2\right)y.

$$\frac{3y^{2}-3y-y+1-3y^{2}+2y}{y\left(y-2\right)\left(y-1\right)}$$

Combine like terms in 3y^{2}-3y-y+1-3y^{2}+2y.

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

Expand y\left(y-2\right)\left(y-1\right).

$$\frac{-2y+1}{y^{3}-3y^{2}+2y}$$

Expand

$$-\frac{1-2y}{y\left(1-y\right)\left(y-2\right)}$$

Short Solution Steps

Factor \left(-y+1\right)\left(-y+2\right).

$$\frac{3y-1}{y\left(y-2\right)}-\frac{3y-2}{\left(-y+1\right)\left(-y+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(y-2\right) and \left(-y+1\right)\left(-y+2\right) is y\left(y-2\right)\left(y-1\right). Multiply \frac{3y-1}{y\left(y-2\right)} times \frac{y-1}{y-1}. Multiply \frac{3y-2}{\left(-y+1\right)\left(-y+2\right)} times \frac{y}{y}.

$$\frac{\left(3y-1\right)\left(y-1\right)}{y\left(y-2\right)\left(y-1\right)}-\frac{\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)}$$

Since \frac{\left(3y-1\right)\left(y-1\right)}{y\left(y-2\right)\left(y-1\right)} and \frac{\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3y-1\right)\left(y-1\right)-\left(3y-2\right)y}{y\left(y-2\right)\left(y-1\right)}$$

Do the multiplications in \left(3y-1\right)\left(y-1\right)-\left(3y-2\right)y.

$$\frac{3y^{2}-3y-y+1-3y^{2}+2y}{y\left(y-2\right)\left(y-1\right)}$$

Combine like terms in 3y^{2}-3y-y+1-3y^{2}+2y.

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

Expand y\left(y-2\right)\left(y-1\right).

$$\frac{-2y+1}{y^{3}-3y^{2}+2y}$$