Solve x^2+7x/2x-6*x^2-10x+21/x^2-49=

$$\frac { x ^ { 2 } + 7 x } { 2 x - 6 } \cdot \frac { x ^ { 2 } - 10 x + 21 } { x ^ { 2 } - 49 } =$$

Evaluate

$$\frac{x}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-10x+21}{x^{2}-49}.

$$\frac{x^{2}+7x}{2x-6}\times \frac{\left(x-7\right)\left(x-3\right)}{\left(x-7\right)\left(x+7\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x^{2}+7x}{2x-6}\times \frac{x-3}{x+7}$$

Multiply \frac{x^{2}+7x}{2x-6} times \frac{x-3}{x+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+7x\right)\left(x-3\right)}{\left(2x-6\right)\left(x+7\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+7\right) in both numerator and denominator.

$$\frac{x}{2}$$

Expand

$$\frac{x}{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-10x+21}{x^{2}-49}.

$$\frac{x^{2}+7x}{2x-6}\times \frac{\left(x-7\right)\left(x-3\right)}{\left(x-7\right)\left(x+7\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x^{2}+7x}{2x-6}\times \frac{x-3}{x+7}$$

Multiply \frac{x^{2}+7x}{2x-6} times \frac{x-3}{x+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+7x\right)\left(x-3\right)}{\left(2x-6\right)\left(x+7\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+7\right) in both numerator and denominator.

$$\frac{x}{2}$$