Solve x^2-18x+81/x^2-5x-36*9x+36/4x^2-38x+18

$$\frac { x ^ { 2 } - 18 x + 81 } { x ^ { 2 } - 5 x - 36 } \cdot \frac { 9 x + 36 } { 4 x ^ { 2 } - 38 x + 18 }$$

Evaluate

$$\frac{9}{2\left(2x-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-18x+81}{x^{2}-5x-36}.

$$\frac{\left(x-9\right)^{2}}{\left(x-9\right)\left(x+4\right)}\times \frac{9x+36}{4x^{2}-38x+18}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x-9}{x+4}\times \frac{9x+36}{4x^{2}-38x+18}$$

Multiply \frac{x-9}{x+4} times \frac{9x+36}{4x^{2}-38x+18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-9\right)\left(9x+36\right)}{\left(x+4\right)\left(4x^{2}-38x+18\right)}$$

Factor the expressions that are not already factored.

$$\frac{9\left(x-9\right)\left(x+4\right)}{2\left(x-9\right)\left(2x-1\right)\left(x+4\right)}$$

Cancel out \left(x-9\right)\left(x+4\right) in both numerator and denominator.

$$\frac{9}{2\left(2x-1\right)}$$

Expand the expression.

$$\frac{9}{4x-2}$$

Expand

$$\frac{9}{2\left(2x-1\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-18x+81}{x^{2}-5x-36}.

$$\frac{\left(x-9\right)^{2}}{\left(x-9\right)\left(x+4\right)}\times \frac{9x+36}{4x^{2}-38x+18}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x-9}{x+4}\times \frac{9x+36}{4x^{2}-38x+18}$$

Multiply \frac{x-9}{x+4} times \frac{9x+36}{4x^{2}-38x+18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-9\right)\left(9x+36\right)}{\left(x+4\right)\left(4x^{2}-38x+18\right)}$$

Factor the expressions that are not already factored.

$$\frac{9\left(x-9\right)\left(x+4\right)}{2\left(x-9\right)\left(2x-1\right)\left(x+4\right)}$$

Cancel out \left(x-9\right)\left(x+4\right) in both numerator and denominator.

$$\frac{9}{2\left(2x-1\right)}$$

Expand the expression.

$$\frac{9}{4x-2}$$