Solve x^2-7x+x^2*7x/left(x^2+7xright)left(x^2-7xright)

$$\frac{ { x }^{ 2 } -7x+ { x }^{ 2 } \times 7x }{ \left( { x }^{ 2 } +7x \right) \left( { x }^{ 2 } -7x \right) }$$

Evaluate

$$\frac{7x^{2}+x-7}{x\left(x^{2}-49\right)}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Factor the expressions that are not already factored.

$$\frac{7x\left(x-\left(-\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)\left(x-\left(\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)}{\left(x-7\right)\left(x+7\right)x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{7\left(x-\left(-\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)\left(x-\left(\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)}{x\left(x-7\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{7x^{2}+x-7}{x^{3}-49x}$$

Expand

$$\frac{7x^{2}+x-7}{x\left(x^{2}-49\right)}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Factor the expressions that are not already factored.

$$\frac{7x\left(x-\left(-\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)\left(x-\left(\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)}{\left(x-7\right)\left(x+7\right)x^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{7\left(x-\left(-\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)\left(x-\left(\frac{1}{14}\sqrt{197}-\frac{1}{14}\right)\right)}{x\left(x-7\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{7x^{2}+x-7}{x^{3}-49x}$$