Solve 9-x^2/x^2-x-42*x^2+8x+12/x^2+2x-15

$$\frac{ 9- { x }^{ 2 } }{ { x }^{ 2 } -x-42 } \times \frac{ { x }^{ 2 } +8x+12 }{ { x }^{ 2 } +2x-15 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{9-x^{2}}{x^{2}-x-42} times \frac{x^{2}+8x+12}{x^{2}+2x-15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9-x^{2}\right)\left(x^{2}+8x+12\right)}{\left(x^{2}-x-42\right)\left(x^{2}+2x-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(-x-3\right)\left(x+2\right)\left(x+6\right)}{\left(x-7\right)\left(x-3\right)\left(x+5\right)\left(x+6\right)}$$

Cancel out \left(x-3\right)\left(x+6\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-x^{2}-5x-6}{x^{2}-2x-35}$$

Expand

$$-\frac{x^{2}+5x+6}{\left(x-7\right)\left(x+5\right)}$$

Short Solution Steps

Multiply \frac{9-x^{2}}{x^{2}-x-42} times \frac{x^{2}+8x+12}{x^{2}+2x-15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9-x^{2}\right)\left(x^{2}+8x+12\right)}{\left(x^{2}-x-42\right)\left(x^{2}+2x-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(-x-3\right)\left(x+2\right)\left(x+6\right)}{\left(x-7\right)\left(x-3\right)\left(x+5\right)\left(x+6\right)}$$

Cancel out \left(x-3\right)\left(x+6\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-x^{2}-5x-6}{x^{2}-2x-35}$$