Solve 5(x/2)-1/9(frac{x{2})-4}

$$\frac { 5 ( \frac { x } { 2 } ) - 1 } { 9 ( \frac { x } { 2 } ) - 4 }$$

Evaluate

$$\frac{5x-2}{9x-8}$$

Short Solution Steps

Express 5\times \frac{x}{2} as a single fraction.

$$\frac{\frac{5x}{2}-1}{9\times \frac{x}{2}-4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{\frac{5x}{2}-\frac{2}{2}}{9\times \frac{x}{2}-4}$$

Since \frac{5x}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-2}{2}}{9\times \frac{x}{2}-4}$$

Express 9\times \frac{x}{2} as a single fraction.

$$\frac{\frac{5x-2}{2}}{\frac{9x}{2}-4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{\frac{5x-2}{2}}{\frac{9x}{2}-\frac{4\times 2}{2}}$$

Since \frac{9x}{2} and \frac{4\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-2}{2}}{\frac{9x-4\times 2}{2}}$$

Do the multiplications in 9x-4\times 2.

$$\frac{\frac{5x-2}{2}}{\frac{9x-8}{2}}$$

Divide \frac{5x-2}{2} by \frac{9x-8}{2} by multiplying \frac{5x-2}{2} by the reciprocal of \frac{9x-8}{2}.

$$\frac{\left(5x-2\right)\times 2}{2\left(9x-8\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5x-2}{9x-8}$$

Expand

$$\frac{5x-2}{9x-8}$$

Short Solution Steps

Express 5\times \frac{x}{2} as a single fraction.

$$\frac{\frac{5x}{2}-1}{9\times \frac{x}{2}-4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{\frac{5x}{2}-\frac{2}{2}}{9\times \frac{x}{2}-4}$$

Since \frac{5x}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-2}{2}}{9\times \frac{x}{2}-4}$$

Express 9\times \frac{x}{2} as a single fraction.

$$\frac{\frac{5x-2}{2}}{\frac{9x}{2}-4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{\frac{5x-2}{2}}{\frac{9x}{2}-\frac{4\times 2}{2}}$$

Since \frac{9x}{2} and \frac{4\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-2}{2}}{\frac{9x-4\times 2}{2}}$$

Do the multiplications in 9x-4\times 2.

$$\frac{\frac{5x-2}{2}}{\frac{9x-8}{2}}$$

Divide \frac{5x-2}{2} by \frac{9x-8}{2} by multiplying \frac{5x-2}{2} by the reciprocal of \frac{9x-8}{2}.

$$\frac{\left(5x-2\right)\times 2}{2\left(9x-8\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5x-2}{9x-8}$$