Solve 3x^2-9x+6/4x^2+4x+12divx^2-4x+3/x^2-8x+15

$$\frac { 3 x ^ { 2 } - 9 x + 6 } { 4 x ^ { 2 } + 4 x + 12 } \div \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 8 x + 15 }$$

Evaluate

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

Short Solution Steps

Divide \frac{3x^{2}-9x+6}{4x^{2}+4x+12} by \frac{x^{2}-4x+3}{x^{2}-8x+15} by multiplying \frac{3x^{2}-9x+6}{4x^{2}+4x+12} by the reciprocal of \frac{x^{2}-4x+3}{x^{2}-8x+15}.

$$\frac{\left(3x^{2}-9x+6\right)\left(x^{2}-8x+15\right)}{\left(4x^{2}+4x+12\right)\left(x^{2}-4x+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(x-5\right)\left(x-3\right)\left(x-2\right)\left(x-1\right)}{4\left(x-3\right)\left(x-1\right)\left(x^{2}+x+3\right)}$$

Cancel out \left(x-3\right)\left(x-1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{2}-21x+30}{4x^{2}+4x+12}$$

Expand

$$\frac{3\left(x^{2}-7x+10\right)}{4\left(x^{2}+x+3\right)}$$

Short Solution Steps

Divide \frac{3x^{2}-9x+6}{4x^{2}+4x+12} by \frac{x^{2}-4x+3}{x^{2}-8x+15} by multiplying \frac{3x^{2}-9x+6}{4x^{2}+4x+12} by the reciprocal of \frac{x^{2}-4x+3}{x^{2}-8x+15}.

$$\frac{\left(3x^{2}-9x+6\right)\left(x^{2}-8x+15\right)}{\left(4x^{2}+4x+12\right)\left(x^{2}-4x+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(x-5\right)\left(x-3\right)\left(x-2\right)\left(x-1\right)}{4\left(x-3\right)\left(x-1\right)\left(x^{2}+x+3\right)}$$

Cancel out \left(x-3\right)\left(x-1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{3x^{2}-21x+30}{4x^{2}+4x+12}$$