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

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

Evaluate

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

Short Solution Steps

Divide 1 by \frac{x}{x^{2}-5x+4} by multiplying 1 by the reciprocal of \frac{x}{x^{2}-5x+4}.

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

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

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

Since \frac{\left(x^{2}-2x\right)x}{x} and \frac{x^{2}-5x+4}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x^{2}-2x\right)x+x^{2}-5x+4.

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

Combine like terms in x^{3}-2x^{2}+x^{2}-5x+4.

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

Differentiate w.r.t. x

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