Solve -6x^-1+(6y)^-1/x^-2

$$\frac { - 6 x ^ { - 1 } + ( 6 y ) ^ { - 1 } } { x ^ { - 2 } }$$

Evaluate

$$\frac{x\left(x-36y\right)}{6y}$$

Short Solution Steps

Expand \left(6y\right)^{-1}.

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

Calculate 6 to the power of -1 and get \frac{1}{6}.

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

Factor the expressions that are not already factored.

$$\frac{\frac{1}{6}\left(-36+\frac{1}{y}x\right)\times \frac{1}{x}}{x^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1}{6}\left(-36+\frac{1}{y}x\right)x^{1}$$

Expand the expression.

$$\frac{1}{6}\times \frac{1}{y}x^{2}-6x$$

Multiply \frac{1}{6} times \frac{1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6y}x^{2}-6x$$

Express \frac{1}{6y}x^{2} as a single fraction.

$$\frac{x^{2}}{6y}-6x$$

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

$$\frac{x^{2}}{6y}+\frac{-6x\times 6y}{6y}$$

Since \frac{x^{2}}{6y} and \frac{-6x\times 6y}{6y} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-6x\times 6y}{6y}$$

Do the multiplications in x^{2}-6x\times 6y.

$$\frac{x^{2}-36xy}{6y}$$

Expand

$$\frac{x^{2}}{6y}-6x$$

Short Solution Steps

Expand \left(6y\right)^{-1}.

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

Calculate 6 to the power of -1 and get \frac{1}{6}.

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

Factor the expressions that are not already factored.

$$\frac{\frac{1}{6}\left(-36+\frac{1}{y}x\right)\times \frac{1}{x}}{x^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1}{6}\left(-36+\frac{1}{y}x\right)x^{1}$$

Expand the expression.

$$\frac{1}{6}\times \frac{1}{y}x^{2}-6x$$

Multiply \frac{1}{6} times \frac{1}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6y}x^{2}-6x$$

Express \frac{1}{6y}x^{2} as a single fraction.

$$\frac{x^{2}}{6y}-6x$$

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

$$\frac{x^{2}}{6y}+\frac{-6x\times 6y}{6y}$$

Since \frac{x^{2}}{6y} and \frac{-6x\times 6y}{6y} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-6x\times 6y}{6y}$$

Do the multiplications in x^{2}-6x\times 6y.

$$\frac{x^{2}-36xy}{6y}$$