Solve x^2-2x-15/3x^2+22x+24*3x^2-14x-24/x^2+8x+15

$$\frac { x ^ { 2 } - 2 x - 15 } { 3 x ^ { 2 } + 22 x + 24 } \cdot \frac { 3 x ^ { 2 } - 14 x - 24 } { x ^ { 2 } + 8 x + 15 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}-2x-15}{3x^{2}+22x+24} times \frac{3x^{2}-14x-24}{x^{2}+8x+15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-2x-15\right)\left(3x^{2}-14x-24\right)}{\left(3x^{2}+22x+24\right)\left(x^{2}+8x+15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-6\right)\left(x-5\right)\left(x+3\right)\left(3x+4\right)}{\left(x+3\right)\left(x+5\right)\left(x+6\right)\left(3x+4\right)}$$

Cancel out \left(x+3\right)\left(3x+4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}-11x+30}{x^{2}+11x+30}$$

Expand

$$\frac{x^{2}-11x+30}{\left(x+5\right)\left(x+6\right)}$$

Short Solution Steps

Multiply \frac{x^{2}-2x-15}{3x^{2}+22x+24} times \frac{3x^{2}-14x-24}{x^{2}+8x+15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-2x-15\right)\left(3x^{2}-14x-24\right)}{\left(3x^{2}+22x+24\right)\left(x^{2}+8x+15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-6\right)\left(x-5\right)\left(x+3\right)\left(3x+4\right)}{\left(x+3\right)\left(x+5\right)\left(x+6\right)\left(3x+4\right)}$$

Cancel out \left(x+3\right)\left(3x+4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}-11x+30}{x^{2}+11x+30}$$