Solve 4x^2+1/x^2-x-2/x-3

$$\frac { 4 x ^ { 2 } + 1 } { x ^ { 2 } } - \frac { x - 2 } { x } - 3$$

Evaluate

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

Short Solution Steps

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

$$\frac{4x^{2}+1}{x^{2}}-\frac{\left(x-2\right)x}{x^{2}}-3$$

Since \frac{4x^{2}+1}{x^{2}} and \frac{\left(x-2\right)x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}+1-\left(x-2\right)x}{x^{2}}-3$$

Do the multiplications in 4x^{2}+1-\left(x-2\right)x.

$$\frac{4x^{2}+1-x^{2}+2x}{x^{2}}-3$$

Combine like terms in 4x^{2}+1-x^{2}+2x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x^{2}}{x^{2}}.

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

Since \frac{3x^{2}+1+2x}{x^{2}} and \frac{3x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 3x^{2}+1+2x-3x^{2}.

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

Expand

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

Short Solution Steps

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

$$\frac{4x^{2}+1}{x^{2}}-\frac{\left(x-2\right)x}{x^{2}}-3$$

Since \frac{4x^{2}+1}{x^{2}} and \frac{\left(x-2\right)x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}+1-\left(x-2\right)x}{x^{2}}-3$$

Do the multiplications in 4x^{2}+1-\left(x-2\right)x.

$$\frac{4x^{2}+1-x^{2}+2x}{x^{2}}-3$$

Combine like terms in 4x^{2}+1-x^{2}+2x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x^{2}}{x^{2}}.

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

Since \frac{3x^{2}+1+2x}{x^{2}} and \frac{3x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 3x^{2}+1+2x-3x^{2}.

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