Solve 9x^2-6x+1/9x^2-3x-3x^2+8x-3/3x^2

$$\frac { 9 x ^ { 2 } - 6 x + 1 } { 9 x ^ { 2 } - 3 x } - \frac { 3 x ^ { 2 } + 8 x - 3 } { 3 x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{9x^{2}-6x+1}{9x^{2}-3x}.

$$\frac{\left(3x-1\right)^{2}}{3x\left(3x-1\right)}-\frac{3x^{2}+8x-3}{3x^{2}}$$

Cancel out 3x-1 in both numerator and denominator.

$$\frac{3x-1}{3x}-\frac{3x^{2}+8x-3}{3x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 3x^{2} is 3x^{2}. Multiply \frac{3x-1}{3x} times \frac{x}{x}.

$$\frac{\left(3x-1\right)x}{3x^{2}}-\frac{3x^{2}+8x-3}{3x^{2}}$$

Since \frac{\left(3x-1\right)x}{3x^{2}} and \frac{3x^{2}+8x-3}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x-1\right)x-\left(3x^{2}+8x-3\right)}{3x^{2}}$$

Do the multiplications in \left(3x-1\right)x-\left(3x^{2}+8x-3\right).

$$\frac{3x^{2}-x-3x^{2}-8x+3}{3x^{2}}$$

Combine like terms in 3x^{2}-x-3x^{2}-8x+3.

$$\frac{-9x+3}{3x^{2}}$$

Factor the expressions that are not already factored in \frac{-9x+3}{3x^{2}}.

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

Cancel out 3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{9x^{2}-6x+1}{9x^{2}-3x}.

$$\frac{\left(3x-1\right)^{2}}{3x\left(3x-1\right)}-\frac{3x^{2}+8x-3}{3x^{2}}$$

Cancel out 3x-1 in both numerator and denominator.

$$\frac{3x-1}{3x}-\frac{3x^{2}+8x-3}{3x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 3x^{2} is 3x^{2}. Multiply \frac{3x-1}{3x} times \frac{x}{x}.

$$\frac{\left(3x-1\right)x}{3x^{2}}-\frac{3x^{2}+8x-3}{3x^{2}}$$

Since \frac{\left(3x-1\right)x}{3x^{2}} and \frac{3x^{2}+8x-3}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x-1\right)x-\left(3x^{2}+8x-3\right)}{3x^{2}}$$

Do the multiplications in \left(3x-1\right)x-\left(3x^{2}+8x-3\right).

$$\frac{3x^{2}-x-3x^{2}-8x+3}{3x^{2}}$$

Combine like terms in 3x^{2}-x-3x^{2}-8x+3.

$$\frac{-9x+3}{3x^{2}}$$

Factor the expressions that are not already factored in \frac{-9x+3}{3x^{2}}.

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

Cancel out 3 in both numerator and denominator.

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