Solve 3x^2+19x+20/9x^2-16*3x^2+8x-16/x^2+x-20

$$\frac { 3 x ^ { 2 } + 19 x + 20 } { 9 x ^ { 2 } - 16 } \cdot \frac { 3 x ^ { 2 } + 8 x - 16 } { x ^ { 2 } + x - 20 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+19x+20}{9x^{2}-16}.

$$\frac{\left(x+5\right)\left(3x+4\right)}{\left(3x-4\right)\left(3x+4\right)}\times \frac{3x^{2}+8x-16}{x^{2}+x-20}$$

Cancel out 3x+4 in both numerator and denominator.

$$\frac{x+5}{3x-4}\times \frac{3x^{2}+8x-16}{x^{2}+x-20}$$

Multiply \frac{x+5}{3x-4} times \frac{3x^{2}+8x-16}{x^{2}+x-20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+5\right)\left(3x^{2}+8x-16\right)}{\left(3x-4\right)\left(x^{2}+x-20\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(3x-4\right)\left(x+5\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+19x+20}{9x^{2}-16}.

$$\frac{\left(x+5\right)\left(3x+4\right)}{\left(3x-4\right)\left(3x+4\right)}\times \frac{3x^{2}+8x-16}{x^{2}+x-20}$$

Cancel out 3x+4 in both numerator and denominator.

$$\frac{x+5}{3x-4}\times \frac{3x^{2}+8x-16}{x^{2}+x-20}$$

Multiply \frac{x+5}{3x-4} times \frac{3x^{2}+8x-16}{x^{2}+x-20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+5\right)\left(3x^{2}+8x-16\right)}{\left(3x-4\right)\left(x^{2}+x-20\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(3x-4\right)\left(x+5\right) in both numerator and denominator.

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