Solve (x ^ 2 - 8x + 15)/(x ^ 2 - 14x + 45) / ((x ^ 2 - 2x - 15)/(x ^ 2 - 8x - 9)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x^{2}-8x+15}{x^{2}-14x+45}\div\frac{x^{2}-2x-15}{x^{2}-8x-9}$$

Evaluate

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

Short Solution Steps

Divide $\frac{x^{2}-8x+15}{x^{2}-14x+45}$ by $\frac{x^{2}-2x-15}{x^{2}-8x-9}$ by multiplying $\frac{x^{2}-8x+15}{x^{2}-14x+45}$ by the reciprocal of $\frac{x^{2}-2x-15}{x^{2}-8x-9}$.

$$\frac{\left(x^{2}-8x+15\right)\left(x^{2}-8x-9\right)}{\left(x^{2}-14x+45\right)\left(x^{2}-2x-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-5\right)\left(x-3\right)\left(x+1\right)}{\left(x-9\right)\left(x+3\right)\left(x-5\right)^{2}}$$

Cancel out $\left(x-9\right)\left(x-5\right)$ in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}-2x-3}{x^{2}-2x-15}$$

Expand

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

Short Solution Steps

Divide $\frac{x^{2}-8x+15}{x^{2}-14x+45}$ by $\frac{x^{2}-2x-15}{x^{2}-8x-9}$ by multiplying $\frac{x^{2}-8x+15}{x^{2}-14x+45}$ by the reciprocal of $\frac{x^{2}-2x-15}{x^{2}-8x-9}$.

$$\frac{\left(x^{2}-8x+15\right)\left(x^{2}-8x-9\right)}{\left(x^{2}-14x+45\right)\left(x^{2}-2x-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-5\right)\left(x-3\right)\left(x+1\right)}{\left(x-9\right)\left(x+3\right)\left(x-5\right)^{2}}$$

Cancel out $\left(x-9\right)\left(x-5\right)$ in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}-2x-3}{x^{2}-2x-15}$$