Solve 3/x^2-7/5x-5

$$\frac { 3 } { x ^ { 2 } } - \frac { 7 } { 5 x - 5 }$$

Evaluate

$$\frac{-7x^{2}+15x-15}{5\left(x-1\right)x^{2}}$$

Short Solution Steps

Factor 5x-5.

$$\frac{3}{x^{2}}-\frac{7}{5\left(x-1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and 5\left(x-1\right) is 5\left(x-1\right)x^{2}. Multiply \frac{3}{x^{2}} times \frac{5\left(x-1\right)}{5\left(x-1\right)}. Multiply \frac{7}{5\left(x-1\right)} times \frac{x^{2}}{x^{2}}.

$$\frac{3\times 5\left(x-1\right)}{5\left(x-1\right)x^{2}}-\frac{7x^{2}}{5\left(x-1\right)x^{2}}$$

Since \frac{3\times 5\left(x-1\right)}{5\left(x-1\right)x^{2}} and \frac{7x^{2}}{5\left(x-1\right)x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 5\left(x-1\right)-7x^{2}}{5\left(x-1\right)x^{2}}$$

Do the multiplications in 3\times 5\left(x-1\right)-7x^{2}.

$$\frac{15x-15-7x^{2}}{5\left(x-1\right)x^{2}}$$

Expand 5\left(x-1\right)x^{2}.

$$\frac{15x-15-7x^{2}}{5x^{3}-5x^{2}}$$

Factor

$$\frac{-7x^{2}+15x-15}{5\left(x-1\right)x^{2}}$$