Solve 4y-1/y/6+frac{3{y}}=

$$\frac { 4 y - \frac { 1 } { y } } { 6 + \frac { 3 } { y } } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4y times \frac{y}{y}.

$$\frac{\frac{4yy}{y}-\frac{1}{y}}{6+\frac{3}{y}}$$

Since \frac{4yy}{y} and \frac{1}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4yy-1}{y}}{6+\frac{3}{y}}$$

Do the multiplications in 4yy-1.

$$\frac{\frac{4y^{2}-1}{y}}{6+\frac{3}{y}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{y}{y}.

$$\frac{\frac{4y^{2}-1}{y}}{\frac{6y}{y}+\frac{3}{y}}$$

Since \frac{6y}{y} and \frac{3}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4y^{2}-1}{y}}{\frac{6y+3}{y}}$$

Divide \frac{4y^{2}-1}{y} by \frac{6y+3}{y} by multiplying \frac{4y^{2}-1}{y} by the reciprocal of \frac{6y+3}{y}.

$$\frac{\left(4y^{2}-1\right)y}{y\left(6y+3\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{4y^{2}-1}{6y+3}$$

Factor the expressions that are not already factored.

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

Cancel out 2y+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4y times \frac{y}{y}.

$$\frac{\frac{4yy}{y}-\frac{1}{y}}{6+\frac{3}{y}}$$

Since \frac{4yy}{y} and \frac{1}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4yy-1}{y}}{6+\frac{3}{y}}$$

Do the multiplications in 4yy-1.

$$\frac{\frac{4y^{2}-1}{y}}{6+\frac{3}{y}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{y}{y}.

$$\frac{\frac{4y^{2}-1}{y}}{\frac{6y}{y}+\frac{3}{y}}$$

Since \frac{6y}{y} and \frac{3}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4y^{2}-1}{y}}{\frac{6y+3}{y}}$$

Divide \frac{4y^{2}-1}{y} by \frac{6y+3}{y} by multiplying \frac{4y^{2}-1}{y} by the reciprocal of \frac{6y+3}{y}.

$$\frac{\left(4y^{2}-1\right)y}{y\left(6y+3\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{4y^{2}-1}{6y+3}$$

Factor the expressions that are not already factored.

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

Cancel out 2y+1 in both numerator and denominator.

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