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

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

Evaluate

$$\frac{5x-7}{\left(x-1\right)^{2}}$$

Short Solution Steps

Factor x^{2}-2x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)^{2} is \left(x-1\right)^{2}. Multiply \frac{4}{x-1} times \frac{x-1}{x-1}.

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

Since \frac{4\left(x-1\right)}{\left(x-1\right)^{2}} and \frac{x-3}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(x-1\right)+x-3.

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

Combine like terms in 4x-4+x-3.

$$\frac{5x-7}{\left(x-1\right)^{2}}$$

Expand \left(x-1\right)^{2}.

$$\frac{5x-7}{x^{2}-2x+1}$$

Expand

$$\frac{5x-7}{\left(x-1\right)^{2}}$$

Short Solution Steps

Factor x^{2}-2x+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)^{2} is \left(x-1\right)^{2}. Multiply \frac{4}{x-1} times \frac{x-1}{x-1}.

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

Since \frac{4\left(x-1\right)}{\left(x-1\right)^{2}} and \frac{x-3}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(x-1\right)+x-3.

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

Combine like terms in 4x-4+x-3.

$$\frac{5x-7}{\left(x-1\right)^{2}}$$

Expand \left(x-1\right)^{2}.

$$\frac{5x-7}{x^{2}-2x+1}$$