Solve 5/4+2/x/frac{4{x}-4/x^2}

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

Evaluate

$$\frac{x\left(5x+8\right)}{16\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{5}{4} times \frac{x}{x}. Multiply \frac{2}{x} times \frac{4}{4}.

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

Since \frac{5x}{4x} and \frac{2\times 4}{4x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 5x+2\times 4.

$$\frac{\frac{5x+8}{4x}}{\frac{4}{x}-\frac{4}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{4}{x} times \frac{x}{x}.

$$\frac{\frac{5x+8}{4x}}{\frac{4x}{x^{2}}-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+8}{4x}}{\frac{4x-4}{x^{2}}}$$

Divide \frac{5x+8}{4x} by \frac{4x-4}{x^{2}} by multiplying \frac{5x+8}{4x} by the reciprocal of \frac{4x-4}{x^{2}}.

$$\frac{\left(5x+8\right)x^{2}}{4x\left(4x-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(5x+8\right)}{4\left(4x-4\right)}$$

Use the distributive property to multiply x by 5x+8.

$$\frac{5x^{2}+8x}{4\left(4x-4\right)}$$

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

$$\frac{5x^{2}+8x}{16x-16}$$

Expand

$$\frac{5x^{2}+8x}{16\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{5}{4} times \frac{x}{x}. Multiply \frac{2}{x} times \frac{4}{4}.

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

Since \frac{5x}{4x} and \frac{2\times 4}{4x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 5x+2\times 4.

$$\frac{\frac{5x+8}{4x}}{\frac{4}{x}-\frac{4}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{4}{x} times \frac{x}{x}.

$$\frac{\frac{5x+8}{4x}}{\frac{4x}{x^{2}}-\frac{4}{x^{2}}}$$

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

$$\frac{\frac{5x+8}{4x}}{\frac{4x-4}{x^{2}}}$$

Divide \frac{5x+8}{4x} by \frac{4x-4}{x^{2}} by multiplying \frac{5x+8}{4x} by the reciprocal of \frac{4x-4}{x^{2}}.

$$\frac{\left(5x+8\right)x^{2}}{4x\left(4x-4\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(5x+8\right)}{4\left(4x-4\right)}$$

Use the distributive property to multiply x by 5x+8.

$$\frac{5x^{2}+8x}{4\left(4x-4\right)}$$

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

$$\frac{5x^{2}+8x}{16x-16}$$