Solve x^2+x+1/4-5x+4/4x

$${ x }^{ 2 } +x+ \frac{ 1 }{ 4 } - \frac{ 5x+4 }{ 4x }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 4x is 4x. Multiply \frac{1}{4} times \frac{x}{x}.

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

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

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

Do the multiplications in x-\left(5x+4\right).

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

Combine like terms in x-5x-4.

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

Factor the expressions that are not already factored in \frac{-4x-4}{4x}.

$$x^{2}+x+\frac{4\left(-x-1\right)}{4x}$$

Cancel out 4 in both numerator and denominator.

$$x^{2}+x+\frac{-x-1}{x}$$

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

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

Since \frac{\left(x^{2}+x\right)x}{x} and \frac{-x-1}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{2}+x\right)x-x-1.

$$\frac{x^{3}+x^{2}-x-1}{x}$$

Expand

$$x^{2}+x-1-\frac{1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 4x is 4x. Multiply \frac{1}{4} times \frac{x}{x}.

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

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

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

Do the multiplications in x-\left(5x+4\right).

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

Combine like terms in x-5x-4.

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

Factor the expressions that are not already factored in \frac{-4x-4}{4x}.

$$x^{2}+x+\frac{4\left(-x-1\right)}{4x}$$

Cancel out 4 in both numerator and denominator.

$$x^{2}+x+\frac{-x-1}{x}$$

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

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

Since \frac{\left(x^{2}+x\right)x}{x} and \frac{-x-1}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{2}+x\right)x-x-1.

$$\frac{x^{3}+x^{2}-x-1}{x}$$