Solve x^2-6x-7/2x^2-98*x^2+14x+49/2x^2+16x+14

$$\frac { x ^ { 2 } - 6 x - 7 } { 2 x ^ { 2 } - 98 } \cdot \frac { x ^ { 2 } + 14 x + 49 } { 2 x ^ { 2 } + 16 x + 14 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-6x-7}{2x^{2}-98}.

$$\frac{\left(x-7\right)\left(x+1\right)}{2\left(x-7\right)\left(x+7\right)}\times \frac{x^{2}+14x+49}{2x^{2}+16x+14}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x+1}{2\left(x+7\right)}\times \frac{x^{2}+14x+49}{2x^{2}+16x+14}$$

Factor the expressions that are not already factored in \frac{x^{2}+14x+49}{2x^{2}+16x+14}.

$$\frac{x+1}{2\left(x+7\right)}\times \frac{\left(x+7\right)^{2}}{2\left(x+1\right)\left(x+7\right)}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{x+1}{2\left(x+7\right)}\times \frac{x+7}{2\left(x+1\right)}$$

Multiply \frac{x+1}{2\left(x+7\right)} times \frac{x+7}{2\left(x+1\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+1\right)\left(x+7\right)}{2\left(x+7\right)\times 2\left(x+1\right)}$$

Cancel out \left(x+1\right)\left(x+7\right) in both numerator and denominator.

$$\frac{1}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$