Solve 3y^-2-y^-1/frac{3{y}-y/3}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 3 is 3y. Multiply \frac{3}{y} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{y}{y}.

$$\frac{3y^{-2}-y^{-1}}{\frac{3\times 3}{3y}-\frac{yy}{3y}}$$

Since \frac{3\times 3}{3y} and \frac{yy}{3y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3y^{-2}-y^{-1}}{\frac{3\times 3-yy}{3y}}$$

Do the multiplications in 3\times 3-yy.

$$\frac{3y^{-2}-y^{-1}}{\frac{9-y^{2}}{3y}}$$

Divide 3y^{-2}-y^{-1} by \frac{9-y^{2}}{3y} by multiplying 3y^{-2}-y^{-1} by the reciprocal of \frac{9-y^{2}}{3y}.

$$\frac{\left(3y^{-2}-y^{-1}\right)\times 3y}{9-y^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out y-3 in both numerator and denominator.

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

Expand the expression.

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

Express -3\times \frac{1}{y} as a single fraction.

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

Express \frac{\frac{-3}{y}}{-y-3} as a single fraction.

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

Use the distributive property to multiply y by -y-3.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 3 is 3y. Multiply \frac{3}{y} times \frac{3}{3}. Multiply \frac{y}{3} times \frac{y}{y}.

$$\frac{3y^{-2}-y^{-1}}{\frac{3\times 3}{3y}-\frac{yy}{3y}}$$

Since \frac{3\times 3}{3y} and \frac{yy}{3y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3y^{-2}-y^{-1}}{\frac{3\times 3-yy}{3y}}$$

Do the multiplications in 3\times 3-yy.

$$\frac{3y^{-2}-y^{-1}}{\frac{9-y^{2}}{3y}}$$

Divide 3y^{-2}-y^{-1} by \frac{9-y^{2}}{3y} by multiplying 3y^{-2}-y^{-1} by the reciprocal of \frac{9-y^{2}}{3y}.

$$\frac{\left(3y^{-2}-y^{-1}\right)\times 3y}{9-y^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out y-3 in both numerator and denominator.

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

Expand the expression.

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

Express -3\times \frac{1}{y} as a single fraction.

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

Express \frac{\frac{-3}{y}}{-y-3} as a single fraction.

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

Use the distributive property to multiply y by -y-3.

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