Solve 3-x/4-2x*x^2+x-6/9-x^2

$$\frac { 3 - x } { 4 - 2 x } \times \frac { x ^ { 2 } + x - 6 } { 9 - x ^ { 2 } }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+x-6}{9-x^{2}}.

$$\frac{3-x}{4-2x}\times \frac{\left(x-2\right)\left(x+3\right)}{\left(x-3\right)\left(-x-3\right)}$$

Extract the negative sign in 3+x.

$$\frac{3-x}{4-2x}\times \frac{-\left(x-2\right)\left(-x-3\right)}{\left(x-3\right)\left(-x-3\right)}$$

Cancel out -x-3 in both numerator and denominator.

$$\frac{3-x}{4-2x}\times \frac{-\left(x-2\right)}{x-3}$$

Multiply \frac{3-x}{4-2x} times \frac{-\left(x-2\right)}{x-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3-x\right)\left(-1\right)\left(x-2\right)}{\left(4-2x\right)\left(x-3\right)}$$

Extract the negative sign in 3-x.

$$\frac{-\left(-1\right)\left(x-3\right)\left(x-2\right)}{\left(x-3\right)\left(-2x+4\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{-\left(-1\right)\left(x-2\right)}{-2x+4}$$

Multiply -1 and -1 to get 1.

$$\frac{x-2}{-2x+4}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -2+x.

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

Cancel out -x+2 in both numerator and denominator.

$$\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$