Solve y+1/y-y-3y-1/

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

Evaluate

$$2y+2+\frac{1}{y}$$

Short Solution Steps

Combine y and -3y to get -2y.

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

Anything divided by one gives itself.

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

To find the opposite of -2y-1, find the opposite of each term.

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

The opposite of -2y is 2y.

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

The opposite of -1 is 1.

$$\frac{y+1}{y}+2y+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2y+1 times \frac{y}{y}.

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

Since \frac{y+1}{y} and \frac{\left(2y+1\right)y}{y} have the same denominator, add them by adding their numerators.

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

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

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

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

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

Expand

$$2y+2+\frac{1}{y}$$

Short Solution Steps

Combine y and -3y to get -2y.

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

Anything divided by one gives itself.

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

To find the opposite of -2y-1, find the opposite of each term.

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

The opposite of -2y is 2y.

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

The opposite of -1 is 1.

$$\frac{y+1}{y}+2y+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2y+1 times \frac{y}{y}.

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

Since \frac{y+1}{y} and \frac{\left(2y+1\right)y}{y} have the same denominator, add them by adding their numerators.

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

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

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

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

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