Solve 8/x-9/frac{6{y}}

$$\frac { \frac { 8 } { x } - 9 } { \frac { 6 } { y } }$$

Evaluate

$$-\frac{3y}{2}+\frac{4y}{3x}$$

Short Solution Steps

Divide \frac{8}{x}-9 by \frac{6}{y} by multiplying \frac{8}{x}-9 by the reciprocal of \frac{6}{y}.

$$\frac{\left(\frac{8}{x}-9\right)y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x}{x}.

$$\frac{\left(\frac{8}{x}-\frac{9x}{x}\right)y}{6}$$

Since \frac{8}{x} and \frac{9x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-9x}{x}y}{6}$$

Express \frac{8-9x}{x}y as a single fraction.

$$\frac{\frac{\left(8-9x\right)y}{x}}{6}$$

Express \frac{\frac{\left(8-9x\right)y}{x}}{6} as a single fraction.

$$\frac{\left(8-9x\right)y}{x\times 6}$$

Use the distributive property to multiply 8-9x by y.

$$\frac{8y-9xy}{x\times 6}$$

Expand

$$-\frac{3y}{2}+\frac{4y}{3x}$$

Short Solution Steps

Divide \frac{8}{x}-9 by \frac{6}{y} by multiplying \frac{8}{x}-9 by the reciprocal of \frac{6}{y}.

$$\frac{\left(\frac{8}{x}-9\right)y}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x}{x}.

$$\frac{\left(\frac{8}{x}-\frac{9x}{x}\right)y}{6}$$

Since \frac{8}{x} and \frac{9x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-9x}{x}y}{6}$$

Express \frac{8-9x}{x}y as a single fraction.

$$\frac{\frac{\left(8-9x\right)y}{x}}{6}$$

Express \frac{\frac{\left(8-9x\right)y}{x}}{6} as a single fraction.

$$\frac{\left(8-9x\right)y}{x\times 6}$$

Use the distributive property to multiply 8-9x by y.

$$\frac{8y-9xy}{x\times 6}$$