Solve 4-5/x/x+frac{3{4x}}

$$\frac { 4 - \frac { 5 } { x } } { x + \frac { 3 } { 4 x } }$$

Evaluate

$$\frac{4\left(4x-5\right)}{4x^{2}+3}$$

Short Solution Steps

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

$$\frac{\frac{4x}{x}-\frac{5}{x}}{x+\frac{3}{4x}}$$

Since \frac{4x}{x} and \frac{5}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x-5}{x}}{x+\frac{3}{4x}}$$

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

$$\frac{\frac{4x-5}{x}}{\frac{x\times 4x}{4x}+\frac{3}{4x}}$$

Since \frac{x\times 4x}{4x} and \frac{3}{4x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x-5}{x}}{\frac{x\times 4x+3}{4x}}$$

Do the multiplications in x\times 4x+3.

$$\frac{\frac{4x-5}{x}}{\frac{4x^{2}+3}{4x}}$$

Divide \frac{4x-5}{x} by \frac{4x^{2}+3}{4x} by multiplying \frac{4x-5}{x} by the reciprocal of \frac{4x^{2}+3}{4x}.

$$\frac{\left(4x-5\right)\times 4x}{x\left(4x^{2}+3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4\left(4x-5\right)}{4x^{2}+3}$$

Use the distributive property to multiply 4 by 4x-5.

$$\frac{16x-20}{4x^{2}+3}$$

Expand

$$\frac{4\left(4x-5\right)}{4x^{2}+3}$$

Short Solution Steps

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

$$\frac{\frac{4x}{x}-\frac{5}{x}}{x+\frac{3}{4x}}$$

Since \frac{4x}{x} and \frac{5}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4x-5}{x}}{x+\frac{3}{4x}}$$

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

$$\frac{\frac{4x-5}{x}}{\frac{x\times 4x}{4x}+\frac{3}{4x}}$$

Since \frac{x\times 4x}{4x} and \frac{3}{4x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x-5}{x}}{\frac{x\times 4x+3}{4x}}$$

Do the multiplications in x\times 4x+3.

$$\frac{\frac{4x-5}{x}}{\frac{4x^{2}+3}{4x}}$$

Divide \frac{4x-5}{x} by \frac{4x^{2}+3}{4x} by multiplying \frac{4x-5}{x} by the reciprocal of \frac{4x^{2}+3}{4x}.

$$\frac{\left(4x-5\right)\times 4x}{x\left(4x^{2}+3\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4\left(4x-5\right)}{4x^{2}+3}$$

Use the distributive property to multiply 4 by 4x-5.

$$\frac{16x-20}{4x^{2}+3}$$