Solve 6x^-1-5y^-1/36x^-2-25y^-2

$$\frac { 6 x ^ { - 1 } - 5 y ^ { - 1 } } { 36 x ^ { - 2 } - 25 y ^ { - 2 } }$$

Evaluate

$$\frac{xy}{5x+6y}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)\times \frac{1}{x}}{\left(-25y^{-2}x^{2}+36\right)x^{-2}}$$

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

$$\frac{\left(-5\times \frac{1}{y}x+6\right)x^{1}}{-25y^{-2}x^{2}+36}$$

Expand the expression.

$$\frac{-5\times \frac{1}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Express -5\times \frac{1}{y} as a single fraction.

$$\frac{\frac{-5}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Express \frac{-5}{y}x^{2} as a single fraction.

$$\frac{\frac{-5x^{2}}{y}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

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

$$\frac{\frac{-5x^{2}}{y}+\frac{6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Since \frac{-5x^{2}}{y} and \frac{6xy}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

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

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{x}{y}\right)^{2}}$$

To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \frac{x^{2}}{y^{2}}}$$

Express -25\times \frac{x^{2}}{y^{2}} as a single fraction.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36+\frac{-25x^{2}}{y^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 36 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}}{y^{2}}+\frac{-25x^{2}}{y^{2}}}$$

Since \frac{36y^{2}}{y^{2}} and \frac{-25x^{2}}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}-25x^{2}}{y^{2}}}$$

Divide \frac{-5x^{2}+6xy}{y} by \frac{36y^{2}-25x^{2}}{y^{2}} by multiplying \frac{-5x^{2}+6xy}{y} by the reciprocal of \frac{36y^{2}-25x^{2}}{y^{2}}.

$$\frac{\left(-5x^{2}+6xy\right)y^{2}}{y\left(36y^{2}-25x^{2}\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y\left(-5x^{2}+6xy\right)}{-25x^{2}+36y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{xy\left(-5x+6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Extract the negative sign in -5x+6y.

$$\frac{-xy\left(5x-6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Cancel out 5x-6y in both numerator and denominator.

$$\frac{-xy}{-5x-6y}$$

Expand

$$\frac{xy}{5x+6y}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)\times \frac{1}{x}}{\left(-25y^{-2}x^{2}+36\right)x^{-2}}$$

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

$$\frac{\left(-5\times \frac{1}{y}x+6\right)x^{1}}{-25y^{-2}x^{2}+36}$$

Expand the expression.

$$\frac{-5\times \frac{1}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Express -5\times \frac{1}{y} as a single fraction.

$$\frac{\frac{-5}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Express \frac{-5}{y}x^{2} as a single fraction.

$$\frac{\frac{-5x^{2}}{y}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

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

$$\frac{\frac{-5x^{2}}{y}+\frac{6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Since \frac{-5x^{2}}{y} and \frac{6xy}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

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

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{x}{y}\right)^{2}}$$

To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \frac{x^{2}}{y^{2}}}$$

Express -25\times \frac{x^{2}}{y^{2}} as a single fraction.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36+\frac{-25x^{2}}{y^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 36 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}}{y^{2}}+\frac{-25x^{2}}{y^{2}}}$$

Since \frac{36y^{2}}{y^{2}} and \frac{-25x^{2}}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}-25x^{2}}{y^{2}}}$$

Divide \frac{-5x^{2}+6xy}{y} by \frac{36y^{2}-25x^{2}}{y^{2}} by multiplying \frac{-5x^{2}+6xy}{y} by the reciprocal of \frac{36y^{2}-25x^{2}}{y^{2}}.

$$\frac{\left(-5x^{2}+6xy\right)y^{2}}{y\left(36y^{2}-25x^{2}\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y\left(-5x^{2}+6xy\right)}{-25x^{2}+36y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{xy\left(-5x+6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Extract the negative sign in -5x+6y.

$$\frac{-xy\left(5x-6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Cancel out 5x-6y in both numerator and denominator.

$$\frac{-xy}{-5x-6y}$$