Solve x^2+12x+35/x^2+4x-5/frac{x^2+3x-28x{7x-7}}

$$\frac{ \frac{ { x }^{ 2 } +12x+35 }{ { x }^{ 2 } +4x-5 } }{ \frac{ { x }^{ 2 } +3x-28x }{ 7x-7 } }$$

Evaluate

$$\frac{7\left(x+7\right)}{x\left(x-25\right)}$$

Short Solution Steps

Divide \frac{x^{2}+12x+35}{x^{2}+4x-5} by \frac{x^{2}+3x-28x}{7x-7} by multiplying \frac{x^{2}+12x+35}{x^{2}+4x-5} by the reciprocal of \frac{x^{2}+3x-28x}{7x-7}.

$$\frac{\left(x^{2}+12x+35\right)\left(7x-7\right)}{\left(x^{2}+4x-5\right)\left(x^{2}+3x-28x\right)}$$

Combine 3x and -28x to get -25x.

$$\frac{\left(x^{2}+12x+35\right)\left(7x-7\right)}{\left(x^{2}+4x-5\right)\left(x^{2}-25x\right)}$$

Factor the expressions that are not already factored.

$$\frac{7\left(x-1\right)\left(x+5\right)\left(x+7\right)}{x\left(x-25\right)\left(x-1\right)\left(x+5\right)}$$

Cancel out \left(x-1\right)\left(x+5\right) in both numerator and denominator.

$$\frac{7\left(x+7\right)}{x\left(x-25\right)}$$

Expand the expression.

$$\frac{7x+49}{x^{2}-25x}$$

Expand

$$\frac{7\left(x+7\right)}{x^{2}-25x}$$

Short Solution Steps

Divide \frac{x^{2}+12x+35}{x^{2}+4x-5} by \frac{x^{2}+3x-28x}{7x-7} by multiplying \frac{x^{2}+12x+35}{x^{2}+4x-5} by the reciprocal of \frac{x^{2}+3x-28x}{7x-7}.

$$\frac{\left(x^{2}+12x+35\right)\left(7x-7\right)}{\left(x^{2}+4x-5\right)\left(x^{2}+3x-28x\right)}$$

Combine 3x and -28x to get -25x.

$$\frac{\left(x^{2}+12x+35\right)\left(7x-7\right)}{\left(x^{2}+4x-5\right)\left(x^{2}-25x\right)}$$

Factor the expressions that are not already factored.

$$\frac{7\left(x-1\right)\left(x+5\right)\left(x+7\right)}{x\left(x-25\right)\left(x-1\right)\left(x+5\right)}$$

Cancel out \left(x-1\right)\left(x+5\right) in both numerator and denominator.

$$\frac{7\left(x+7\right)}{x\left(x-25\right)}$$

Expand the expression.

$$\frac{7x+49}{x^{2}-25x}$$